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Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) stability theory; Zariski topologies over an algebraically closed field; Zariski geometry; dimension; smooth algebraic variety; algebraic curve; ample; finite covers of the projective line Hrushovski E. and Zilber B., Zariski geometries, J. Amer. Math. Soc. 9 (1996), 1-56. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) L-functions; p-divisibility of certain exponential sums over finite fields; theorem of Chevalley-Warning Adolphson, A.; Sperber, S., \(p\)-Adic estimates for exponential sums and the theorem of Chevalley-Warning, Ann. Sci. Ècole Norm. Sup., 20, 545-556, (1987) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) geometric approach to Eichler's arithmetic theory of definite quaternion algebras; modular forms of weight 3/2; Waldspurger's formula; elliptic curves with prime conductor; critical values of L-series; weight two cusp form; special points; height pairing B. H. Gross, ''Heights and the special values of \(L\)-series,'' in Number Theory, Providence, RI: Amer. Math. Soc., 1987, vol. 7, pp. 115-187. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) elementary number theory; symmetric cryptosystems; DES-algorithm; secure block cipher; public key cryptosystems; prime number generation; primality tests; integer factorization; discrete logarithm; cryptographic hash functions; authentication codes; digital signature; Merkle's signature scheme; Lamport-Diffie-one-time signature scheme; finite fields and elliptic curves; identification; challenge-response-identification; zero-knowledge proofs; Shannon's theory; secret sharing; AES-algorithm; Rijndael cipher | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraic function fields; algebraic curves; Riemann-Roch theorem; coding theory; algebraic-geometry codes; differentials; towers of functions fields; Tsfasman-Vladut-Zink theorem; trace codes Stichtenoth, H., \textit{Algebraic Function Fields and Codes}, 254, (2009), Springer, Berlin | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert functions; Betti numbers; fibers of flat family of closed subschemes M. Boratyński and S. Greco, Hilbert functions and Betti numbers in a flat family, Ann. Mat. Pura Appl. (4) 142 (1985), 277 -- 292 (1986). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) analytic moduli problems; deformation of complex structures; Kodaira-Spencer map; Kuranishi spaces; period mappings; Hodge theory; mixed Hodge structures; Jacobian varieties; Torelli's theorem; theta functions; non-abelian conformal field theory Shimizu, Y.; Ueno, K., Advances in moduli theory, (2002), AMS | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) intersection theory; Roth's formulas; polar classes of a threefold | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Frobenius classes; volumes of tubes; semi-algebraic set; prime number theorem in algebraic number fields; Chebotarev's density theorem; equidistribution of prime ideals B. Z. Moroz, ''Equidistribution of Frobenius classes and the volumes of tubes,'' Acta Arith., 51, 269--276 (1988). | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraically closed fields; real closed fields; quantifier elimination; diagrams | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) positive characteristic; extremal rays; Mori's structure theorem for threefolds; deformation theory of curves in smooth threefolds Kollár, Ann. Sci. Éc. Norm. Supér. (4) 24 pp 339-- (1991) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Abstract theory of rings, fields, etc. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) locally nilpotent derivations; additive group actions; Hilbert's Fourteenth Problem G. Freudenburg, \textit{Algebraic Theory of Locally Nilpotent Derivations}, Encyclopaedia of Mathematical Sciences, Vol. 136, Springer Berlin, 2006. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) derived scheme; connective pro-cotangent space; connective deformation theory; almost of finite type (pro-)quasicoherent sheaf; anchor map; Chevalley functor; ind scheme; cocommutative Hopf algebra; cocommutative bi-algebra; co-operad; composition monoidal structure; crystal; de Rham prestack; differential of $x$; exponential map; filtered object; formal moduli problem; formally smooth; Hodge filtration; ind-inf-scheme; inertia object; Lie operad; left-Lax equivariance; $n$-coconnective ind-scheme; pro-cotangent complex; reduced indscheme; shifted anchor map; smooth of relative dimension $n$; splitting of a Lie algebroid; universal envelope of a Lie algebra; Verdier duality; Weil restriction; zero Lie algebroid | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Nash's problem on arcs; surfaces; singularities; resolution of singularities; space of arcs; wedges | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) ''residue homomorphism''; completion of Milnor's higher K-groups; reciprocity map; higher-dimensional class field theory K. Kato : Residue homomorphisms in Milnor K-theory . Adv. St. Pure Math. 2 (1983) 153-172. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Topology; Ergodic theory; Real algebraic geometry; Rokhlin's memorial | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) symbolic powers of ideals; Waldschmidt constants; Hilbert functions; weak Lefschetz property; Verlinde formula; Demailly's conjecture | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) finite groups; rational invariants; matrix normal form; polynomial system reduction; constructive Noether's problem Hubert, Evelyne; Labahn, George, Computation of invariants of finite abelian groups, Math. Comp., 0025-5718, 85, 302, 3029-3050, (2016) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) sums of squares; positive semi-definite quadratic forms; Pythagoras numbers; sums of squares multipliers | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraic curves over finite prime fields; points of algebraic varieties over finite prime fields; existence of rational points; distribution of arithmetic sequences; distribution of angles of Kloosterman sums; verification of distribution functions; density functions of distributions | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) hypersurfaces; polynomial endomorphisms; real closed fields; quadratic forms | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) number of cells; real closed field Saugata Basu, Richard Pollack, and Marie-Françoise Roy, On the number of cells defined by a family of polynomials on a variety, Mathematika 43 (1996), no. 1, 120 -- 126. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Lie algebroid; dg-Lie algebra; formal moduli problem; Koszul duality; deformation theory; derived infinitesimal thickening; Kodaira-Spencer; space of extensions; Schlessinger conditions; connective commutative \(k\)-algebra; formal moduli problem; small extensions; \(\infty\)-category of Lie algebroids; ind-coherent sheaves; pro-coherent sheaves; pro-coherent formal moduli problem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Waring problem; Sylvester algorithm; Hilbert function; secant varieties; apolarity theory | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) number of rational points; trace code; Artin-Schreier curve; generalized Hamming weights; survey G. van der Geer and M. van der Vlugt, How to construct curves over finite fields with many points, in \textit{Arithmetic Geometry (Cortona, 1994)}, Symposia Mathematica Cambridge: Cambridge University Press, 37 (1997), 169-189. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) sums of squares; symmetric polynomials; Gram spectrahedron; semidefinite programming | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) reduction theory; parametrization; norm equation; torsion groups of elliptic curves; integral \(j\)-invariant; cubic fields; Gröbner basis; elimination Pethö, Attila; Weis, Thomas; Zimmer, Horst G., Torsion groups of elliptic curves with integral \(j\)-invariant over general cubic number fields, Internat. J. Algebra Comput., 7, 3, 353-413, (1997) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Jacobi sums; Fermat curves; \(p\)-adic cohomology; Fontaine's theory | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Schlessinger's theory of deformations; geometric deformation stacks; groupoids; tangent space and obstructions | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's tenth problem; elliptic curves; Mazur's conjecture | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) equivalence of ideal topologies; uniform equivalence; uniform Artin-Rees Lemma; Chevalley's Theorem Huneke, C.; Katz, D.; Validashti, J., Uniform equivalence of symbolic and adic topologies, Ill. J. Math., 53, 325-338, (2009) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real closed valued fields; \(o\)-minimality; \(T\)-convex fields; \(t\)-stratifications; Jacobian property; \(b\)-minimality; Whitney stratifications | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Brauer groups of schemes; finite ground fields; arithmetic ground fields; motivic cohomology; motivic homotopy theory | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Göttsche's universality conjecture; curve counting; Hilbert scheme of points; singularities; algebraic cobordism; degeneration methods; Severi variety J. Li and Y. Tzeng, Universal polynomials for singular curves on surfaces , preprint, [math.AG]. arXiv:1203.3180v1 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) positive polynomial; sum of squares; moment problem; combinatorial optimization; semidefinite optimization; polynomial optimization M. Laurent, \textit{Optimization over polynomials: Selected topics}, in Proceedings of the International Congress of Mathematicians (ICM 2014), 2014, pp. 843--869. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Galois stratification; field arithmetic; Dwork cohomology; \(\ell\)-adic cohomology; Chow motives; Chebotarev density; Davenport's problem; Felgner's problem; Poincaré series; difference fields | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) local fields; asymptotic expansion of fibre integrals; oscillating integrals; residues of poles of Igusa's local zeta-functions [D-J] J. Denef and P. Jacobs,On the vanishing of principal value integrals, C. R. Acad. Sci. Paris, Sér. I326 (1998), 1041--1046. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) maximal 2-extension; Galois group; Pythagorean closure; formally real field; SAP-field; Brauer group of a pseudo-real closed field | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) real analytic space; global Nullstellensatz; 17th Hilbert problem | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) finite group; G-space; Steenrod's problem; realizable RG-module; Frobenius-closed homogeneous subvarieties; cohomological equivalence class DOI: 10.1016/0022-4049(87)90013-2 | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Fuchsian groups; Weierstrass points; real algebraic geometry; birational automorphism groups of real curves; Siegel modular group; NEC groups; Teichmüller spaces; uniformization theory for Klein surfaces; automorphism groups of real algebraic curves \textsc{E. Bujalance, J. J. Etayo, J. M. Gamboa, and}\textsc{G. Gromadzki}, Automorphism Groups of Compact Bordered Klein Surfaces. A Combinatorial Approach, Lecture Notes in Mathematics, 1439, Springer-Verlag, Berlin, 1990. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) algebraic curves; finite fields; Artin-Schreier type curves; rational points | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) homotopy theory; semi-algebraic spaces; real closed field | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) function fields of conics; Zariski problem; transcendental extension; rationality; regular function field; Amitsur-MacRae theorem Jack Ohm, Function fields of conics, a theorem of Amitsur-MacRae, and a problem of Zariski, Algebraic geometry and its applications (West Lafayette, IN, 1990) Springer, New York, 1994, pp. 333 -- 363. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) compactification of the moduli space of curves; geometric invariant theory; Chow variety; Hilbert scheme; stable curves D. Schubert, ''A new compactification of the moduli space of curves,'' Compositio Math., vol. 78, iss. 3, pp. 297-313, 1991. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) ordered rings with involution; \(C^*\)-algebras and their representations; noncommutative convexity theory; real algebraic geometry Jakob Cimprič, A representation theorem for Archimedean quadratic modules on *-rings, Canad. Math. Bull. 52 (2009), no. 1, 39 -- 52. | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert scheme of points; representation theory | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Hilbert's program; constructive proofs; geometric theories; classical abstract objects; distributive lattices; pointfree topological spaces; spectral spaces; Krull dimension; constructive mathematics; dynamical algebraic structures Lombardi, H., Algèbre dynamique, espaces topologiques sans points et programme de Hilbert, Ann. Pure Appl. Logic, 137, 256-290, (2006) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) constructive mathematics; Nullstellensatz; Positivstellensatz; algebraically closed valued fields; ordered groups; geometric conditions; dynamical proofs; simultaneous collapse Coste, Michel; Lombardi, Henri; Roy, Marie-Françoise, Dynamical method in algebra: effective Nullstellensätze, Ann. Pure Appl. Logic, 111, 3, 203-256, (2001) | 1 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) arithmetical ring; Bézout ring; coherent ring; constructive; Hilbert's program; local-global; \(pp\)-ring; projective module; Prüfer ring; Quillen-Suslin; rereading principle Lombardi, H.; Quitté, C.; Yengui, I., Hidden constructions in abstract algebra (6) the theorem of maroscia, brewer and costa, J. pure appl. algebra, 212, 1575-1582, (2008) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) Lombardi, H., \textit{hidden constructions in abstract algebra. I. integral dependance}, Journal of Pure and Applied Algebra, 167, 259-267, (2002) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) constructive mathematics; Lequain-Simis induction theorem; Quillen-Suslin theorem; finitely generated projective modules; local-global principles; Prufer domains; arithmetical rings A. Ellouz, H. Lombardi, I. Yengui, A constructive comparison between the rings R(X) and R\langleX\rangle and application to the Lequain-Simis induction theorem, J. Algebra (in press) | 0 |
Hilbert's seventeenth problem; Artin-Schreier theory; constructive mathematics; sums of squares; real fields; ordered fields; real closed fields; dynamic evaluation Lombardi, H., Relecture constructive de la théorie d'artin-Schreier, Ann. pure appl. logic, 91, 59-92, (1998) henselization; constructive mathematics; valued field; Newton polygon F.-V. Kuhlmann, S. Kuhlmann, Explicit construction of exponential-logarithmic power series, preprint. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite subgroup of \(Sl(2,\mathbb{C})\); simple singularities; Dynkin diagram; homology of minimal resolution; root system; Cartan matrix; simple Lie group; McKay correspondence; Coxeter number | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite-dimensional vector space; class; finite group; composition series; alternative groups; groups of Lie type; simple groups; algebra of invariant polynomial functions; semisimple algebraic group; Weyl group N. L. Gordeev, Coranks of elements of linear groups and the complexity of algebras of invariants, Algebra i Analiz 2 (1990), no. 2, 39 -- 64 (Russian); English transl., Leningrad Math. J. 2 (1991), no. 2, 245 -- 267. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite-dimensional vector space; class; finite group; composition series; alternative groups; groups of Lie type; simple groups; algebra of invariant polynomial functions; semisimple algebraic group; Weyl group Gordeev, N.: Coranks of elements of linear groups and the complexity of algebras of invariants. Leningrad math. J. 2, 245-267 (1991) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. dimension types; indecomposables of arbitrary quivers; finite representation type; extended Dynkin diagram; indecomposable representations; positive roots; Tits form; tame; Kac's theorem; affine varieties; orbits; simple roots; reflections; Dynkin quiver; root system H. Kraft and Ch. Riedtmann, Geometry of representations of quivers, Representations of algebras (Durham, 1985) London Math. Soc. Lecture Note Ser., vol. 116, Cambridge Univ. Press, Cambridge, 1986, pp. 109 -- 145. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite group schemes; coordinate algebras; modules of constant Jordan type; \(W\)-modules; equal images property; modular representations; Grothendieck groups Carlson, J. F.; Friedlander, E. M.; Suslin, A. A., Modules for \(\mathbb{Z} / p \times \mathbb{Z} / p\), Comment. Math. Helv., 86, 609-657, (2011) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finitely generated algebras; algebraic variety; \(\text{Gl}_ d\)-actions; algebras of finite representation type; pointed varieties; minimal degenerations; minimal singularities; representations of Dynkin quivers; nilpotent matrices; tilting modules; tilting theories; Gabriel quivers; preprojective modules Bongartz, K.: Minimal singularities for representations of Dynkin quivers. Comment. Math. Helv. 69(4), 575--611 (1994) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Dynkin diagram; simple Lie groups; simple singularities; representations of Weyl groups; monodromy transformations Slodowy, P., Four lectures on simple groups and singularities, \textit{Communications of the Math. Institute}, (1980) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. algebraic surfaces; action of finite groups; resolution of singularities; Heisenberg algebra; Virasoro algebra; representation of Lie algebras; vertex algebras; equivariant \(K\)-theory of schemes W. Wang, Algebraic structures behind Hilbert schemes and wreath products, in: S. Berman et al. (Eds.), Recent Developments in Infinite-Dimensional Lie Algebras and Conformal Field Theory, Charlottesville, VA, 2000; Contemp. Math. 297 (2002) 271-295. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite groups of automorphisms; symplectic vector spaces; multi-parameter deformations; symplectic reflection algebras; coordinate rings; McKay correspondence; Weyl groups; double affine Hecke algebras; Harish-Chandra homomorphisms; invariant polynomial differential operators; Calogero-Moser differential operators P. Etingof and V. Ginzburg, Symplectic reflection algebras, Calogero--Moser space, and deformed Harish-Chandra homomorphism, \textit{Invent. Math.}, 147 (2002), no. 2, 243--348. Zbl 1061.16032 MR 1881922 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. representation types; Dynkin diagrams; quivers; representations of finite group schemes; cohomological support varieties; indecomposable modules; cocommutative Hopf algebras; module categories; finite representation type | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. conjugacy classes; representation theory of finite groups of Lie type; connected reductive algebraic group; Frobenius morphism; finite group of F-fixed points; BN-pair; Weyl group; Borel subgroup; maximal torus; intersections of parabolic subgroups; virtual representation; generalized character; \(\ell \)-adic cohomology; flag variety; geometric conjugacy; Jordan decomposition; unipotent elements; Deligne-Lusztig characters; irreducible characters; regular characters; Gelfand-Graev representation; cuspidal characters; unipotent characters; intersection cohomology; Springer correspondence; representations of Coxeter groups; Dynkin diagrams; bibliography; exceptional groups; character tables R.\ W. Carter, Finite Groups of Lie Type: Conjugacy Classes and Complex Characters, John Wiley, New York, 1985. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite Chevalley groups; finite groups of Lie type; Frobenius kernels; Parshall conjecture; projective modules; restricted Lie algebras; semisimple algebraic group schemes; restricted Lie algebras; restricted enveloping algebras; complexity of modules; Borel subgroups; unipotent radical Drupieski, CM, On projective modules for Frobenius kernels and finite Chevalley groups, Bull. Lond. Math. Soc., 45, 715-720, (2013) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. module schemes; orbit closures; smooth morphisms; Grothendieck groups; Dynkin quivers; representations of finite-dimensional algebras Zwara, G.: Smooth morphisms of module schemes. Proc. Lond. Math. Soc. (3) 84(3), 539--558 (2002) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. \(K3\) surfaces; Chow groups; Hilbert schemes of points; Lie algebras | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Weyl groups; Coxeter groups; representations of Hecke algebras; Jordan-Hölder series of Verma modules; irreducible highest weight modules; Weyl character formula; primitive ideals in enveloping algebras; complex semisimple Lie algebras; local Poincaré duality; geometry of Schubert cells; flag varieties; intersection cohomology; Laurent polynomials; intertwining operators; finite Chevalley groups; affine Weyl groups; cohomology groups; simple reflections; highest weight representations; Cartan subalgebras D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, \textit{Invent.} \textit{Math.}, 53 (1979), no. 2, 165--184.Zbl 0499.20035 MR 560412 | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. torsors; Galois extensions; representations of restricted Lie algebras; quantum groups; finite-dimensional Hopf algebras; affine schemes; cocommutative Hopf algebras; Miyashita-Ulbrich actions; equivariant splittings; sheaves; faithfully flat descent [Ru1] D. Rumynin,Hopf-Galois extensions with central invariants and their geometric properties, Alg. Rep. Th.,1 (1998), 353--381. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. representation theory; reductive algebraic groups; simple modules; highest weights; character formulas; Weyl's character formula; affine group schemes; injective modules; injective resolutions; derived functors; Hochschild cohomology groups; hyperalgebra; split reductive group schemes; Steinberg's tensor product theorem; irreducible representations; Kempf's vanishing theorem; Borel-Bott-Weil theorem; characters; linkage principle; dominant weights; filtrations; Steinberg modules; cohomology rings; rings of regular functions; Schubert schemes; line bundles; Schur algebras; quantum groups; Kazhdan-Lusztig polynomials J. C. Jantzen, \textit{Representations of Algebraic Groups. Second edition}, Amer. Math. Soc., Providence (2003). | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hilbert schemes of points; quantum affine algebras; quantum dimensions; simple surface singularities | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Bruhat-Chevalley orders; Bruhat-Renner decompositions; Cohen-Macaulay rings; conjugacy classes; finite groups of Lie type; finite monoids of Lie type; Gorenstein rings; Hecke algebras; Kazhdan-Lusztig polynomials; linear algebraic monoids; reductive groups; reductive monoids; Putcha lattices of cross-sections; Renner monoids; representation theory; shellability; Stanley-Reisner rings; Weyl groups | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. strict simple degenerations; geometric Invariant theory; Hilbert schemes; good minimal dlt models; type II degenerations of \(K3\) surfaces | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. group schemes; cohomological support varieties; restricted Lie algebras; complexity; \(\pi\)-points; Weil restriction; projectivity; finite Chevalley groups; non-maximal support varieties; constant Jordan type Eric M. Friedlander, Weil restriction and support varieties, J. Reine Angew. Math. 648 (2010), 183 -- 200. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Kleinian singularities; McKay correspondence; Lie algebras; derived category of coherent sheaves; Hall algebra; Kac-Moody Lie algebra M. Kapranov and E. Vasserot, Kleinian singularities, derived categories and hall algebras, Math. Ann. 316 (2000), no. 3, 565-576. | 1 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. moduli space of curves; moduli space of principally polarized abelian varieties; mapping class groups; unipotent completion; Hodge Lie algebra; presentation of nilpotent Lie algebras; classical modular forms; special values of L-functions | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. orbits; simple singularities; modular invariant partition functions; root systems; hypersurface singularities | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. logarithmic signatures; finite groups of Lie type; simple groups; Singer groups Singhi, [Singhi et al. 10] N.; Singhi, N.; Magliveras., S., Minimal logarithmic signatures for finite groups of Lie type., \textit{Des. Codes Cryptogr.}, 55, 2-3, 243-260, (2010) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. support varieties; finite group schemes; \(\pi\)-points; coordinate algebras; modules of constant Jordan type; modular representations Eric M. Friedlander and Julia Pevtsova, Generalized support varieties for finite group schemes, Doc. Math. Extra vol.: Andrei A. Suslin sixtieth birthday (2010), 197 -- 222. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Chevalley group schemes; algebraic groups; finite groups of Lie type; classifying stacks; \(\ell\)-adic cohomology | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. subregular classes; Dynkin curves; orbital varieties; simple algebraic groups; Borel subgroups; adjoint actions; Springer fibers; Lie algebras; irreducible components; numbers of orbits Goodwin, SM; Hille, L; Röhrle, G, The orbit structure of Dynkin curves, Math. Z., 257, 439-451, (2007) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. quotient singularities; McKay correspondence; Hilbert schemes; polyhedral groups Boissière, S.; Sarti, A., Contraction of excess fibres between the McKay correspondences in dimensions two and three, Ann. Inst. Fourier (Grenoble), 57, 1839-1861, (2007) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. invariant theory for Kleinian groups; simple elliptic singularities; systems of regular weights; polyhedral group; extended Dynkin diagrams; Coxeter transformation; Weyl group; Heisenberg groups; Fuchsian groups Saito, K.: Around the theory of the generalized weight system: relations with singularity theory, the generalized Weyl group and its invariant theory, etc.. Sugaku 38, 97-115 (1986) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. tame algebras; support varieties; representations of Hopf algebras; tame representation type; complexity of finite-dimensional modules; finite group schemes; cocommutative Hopf algebras; reduced enveloping algebras; restricted Lie algebras Farnsteiner, Rolf, Tameness and complexity of finite group schemes, Bull. Lond. Math. Soc., 39, 1, 63-70, (2007) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. faithful dimension of finite groups; Kirillov's orbit method; Lazard correspondence; Frobenius sets; free nilpotent Lie algebras | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Hilbert schemes; spectral curves; integrable systems on loop algebras and loop groups; Lie-Poisson group structure; abelianisation; separation of variables; integrable Hamiltonian systems Hurtubise, J.; Markman, E., Surfaces and the Sklyanin bracket, Commun. Math. Phys., 230, 485-502, (2002) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. characterization of p-adic analytic groups; projective limit of finite p-groups; totally discontinuous compact groups; correspondence with Lie algebras; cohomological dimension; continuous cohomology; analytic cohomology; cohomology of Lie algebras M. Lazard, Groupes analytiques \textit{p}-adiques, Inst. Hautes Études Sci. Publ. Math. (1965), no. 26, 389-603. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. nilpotent orbits; symplectic singularities; Slodowy slice; Dynkin diagrams; Dynkin classification; transverse slice; generic singularities; degenerate orbits; closure relation; simple singularities,isolated singularities; simple surface singularities; generic orbits; generic singularities; exceptional Lie algebras; Springer correspondence B. Fu, D. Juteau, P. Levy and E. Sommers, \textit{Generic singularities of nilpotent orbit closures}, [arXiv:1502.05770]. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. group algebras of finite groups; finitely generated algebras; Morita equivalences; quivers; degenerations of modules; decomposable modules; biserial algebras; representation type | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite groups of Lie type; generic Cartan invariants; Frobenius kernels; group schemes | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. linear algebraic monoids; linear algebraic groups; groups of units; Zariski closed submonoids; total matrix monoids; idempotents; maximal tori; reductive monoids; Weyl groups; weights; roots; parabolic subgroups; Tits buildings; Putcha cross section lattices; Renner monoids; reductive algebraic groups; finite reductive monoids; \(BN\)-pairs; Borel subgroups; Bruhat decompositions; finite groups of Lie type; finite monoids of Lie type; finite reductive groups; Frobenius maps; Hecke algebras Louis Solomon, An introduction to reductive monoids, Semigroups, formal languages and groups (York, 1993) NATO Adv. Sci. Inst. Ser. C Math. Phys. Sci., vol. 466, Kluwer Acad. Publ., Dordrecht, 1995, pp. 295 -- 352. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. quivers of type \(A\); representation spaces; Ringel-Hall algebras; canonical bases; categories of representations; symmetric functions; quantum groups; flag varieties; nilpotent orbits; Schubert varieties; Kazhdan-Lusztig polynomials; Schur-Weyl duality; affine Hecke algebras Schiffmann, O., Quivers of type \textit{A}, flag varieties and representation theory, Fields inst. commun., vol. 40, 453-479, (2004), Amer. Math. Soc. Providence, RI | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. word maps; random walks on finite simple groups; groups of Lie type | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite fields; character sums; Weil conjectures; Riemann-Roch theorem; points on curves over finite fields; zeta-functions; \(L\)-functions; idele class characters; modular forms; automorphic representations; Ramanujan graphs; Alon-Boppana theorem; regular graphs; Riemann hypothesis for zeta functions of curves over finite fields; exponential sums; Cayley graphs; finite upper half plane graphs; valuations of function fields; projective curve; Hecke operators; automorphic representations of quaternion groups; expander; simple random walk; spectral theory of graphs Li, W. -C. Winnie: Number theory with applications. Series of university mathematics 7 (1996) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. Coxeter groups; reflection arrangements; cones; posets; characteristic polynomials; lattices; distance functions; freeness; real hyperplane arrangements; lunes; Braid arrangements; descent and lune equations; Varchenko matrices; Birkhoff algebras; Tits algebras; Lie and Zie elements; Eulerian idempotents; homologies and cohomologies; Loewy series; Dynkin idempotents; Incidence algebras; Invariant algebras; Moebius functions , Hyperplane Arrangements, Universitext, Springer, Cham, 2017. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite group schemes; modules of constant Jordan type; exact categories; group algebras; Grothendieck groups; categories of finitely generated projective modules; thickenings; stable module categories; Frobenius kernels Jon F. Carlson and Eric M. Friedlander, Exact category of modules of constant Jordan type, Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. I, Progr. Math., vol. 269, Birkhäuser Boston, Inc., Boston, MA, 2009, pp. 267 -- 290. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. affine Lie algebras; abelian varieties; modular invariant; partition function; rational conformal field theory; Jacobian of a Fermat curve; triangulated surfaces; Riemann surface M. Bauer, A. Coste, C. Itzykson and P. Ruelle, ''Comments on the links between SU(3) modular invariants, simple factors in the Jacobian of Fermat curves, and rational triangular billiards,'' J. Geom. Phys. 22 (1997), 134--189. | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. finite group schemes; modules over finite group schemes; modules of constant Jordan type; group algebras; almost split sequences; Auslander-Reiten quivers Carlson J.F., Friedlander E.M., Pevtsova J.: Modules of constant Jordan type. J. Reine \& Angew. Math. 614, 191--234 (2008) | 0 |
simple singularities; McKay correspondence; Hilbert schemes; simple Lie groups; simple Lie algebras; quivers of finite type; modular invariant partition functions; von Neumann algebras; Dynkin diagram Y. Ito, I. Nakamura, \textit{Hilbert schemes and simple singularities}, in: \textit{New Trends in Algebraic Geometry} (Warwick, 1996), London Math. Soc. Lecture Note Ser., Vol. 264, Cambridge Univ. Press, Cambridge, 1999, pp. 151-233. semigroups of upper triangular matrices; finite regular monoids; unit groups; algebras of invariants; complex semigroup algebras; irreducible characters; induced characters; quasi-hereditary algebras; cuspidal characters; canonical monoids of Lie type; balanced monoids; full transformation semigroups Putcha M., J. Algebra 163 pp 632-- | 0 |
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