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noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Cayley-Bacharach theorem; complete intersections; Hilbert function of graded Gorenstein algebras Davis, Gorenstein algebras and the Cayley-Bacharach theorem, Proc. Amer. Math. Soc. 93 pp 593-- (1985) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) monomialization; field extension of two-dimensional function fields Cutkosky, S.D., Piltant, O.: Monomial resolutions of morphisms of algebraic surfaces. Special issue in honor of Robin Hartshorne. Commun. Algebra 28, 5935--5959 (2000) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) curves defined over a valuation ring; function field; first order language of valued fields; stable reduction theorem [GMP] B. W. Green, M. Matignon and F. Pop,On valued function fields III, Reductions of algebraic curves, Journal für die Reine und Angewandte Mathematik432 (1992), 117--133. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) division algebras; Brauer groups; degrees; indices; \(p\)-adic curves; algebraic function fields Eric Brussel, On Saltman's \?-adic curves papers, Quadratic forms, linear algebraic groups, and cohomology, Dev. Math., vol. 18, Springer, New York, 2010, pp. 13 -- 39. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) covering spaces of projective manifolds; ample line bundle; holomorphic functions of slow growth; Riemann surfaces with corona; generating Hörmander algebras on covering spaces; dichotomy; covering group; harmonic functions; weighted Bergman spaces Finnur Lárusson, Holomorphic functions of slow growth on nested covering spaces of compact manifolds, Canad. J. Math. 52 (2000), no. 5, 982 -- 998. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) graded Clifford algebras; skew Clifford algebras; twists of Clifford algebras; regular algebras; quadric systems; quadratic algebras Nafari, M.; Vancliff, M., Graded skew Clifford algebras that are twists of graded Clifford algebras, Communications in Algebra, 43, 719-725, (2015) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) \(K_ 2\) of fields; Brauer group; cyclic algebras; generators Merkurjev, A. S.: On the structure of the Brauer group of fields. Math. USSR izv. 27, No. 1, 141-157 (1986) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Brauer groups of fields; elements of exponent p; classes of cyclic algebras of degree p A. S. Merkurjev, Brauer groups of fields, Comm. Algebra 11 (1983), 2611--2624. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) rational surfaces; ruled surfaces; Néron-Severi group; blowing-up; Picard number of an algebraic surface | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) valued function fields; existence of regular functions; Henselian constant field; divisor reduction map; divisor group; elementary class Green, B.; Matignon, M.; Pop, F.: On valued function fields II: Regular functions and elements with the uniqueness property. J. reine angew. Math. 412, 128-149 (1990) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Brauer group of function field; reciprocity sequence; higher-dimensional function fields; smooth projective varieties; threefolds J. -L. Colliot-Thélène, ''On the reciprocity sequence in the higher class field theory of function fields,'' in Algebraic \(K\)-Theory and Algebraic Topology, Dordrecht: Kluwer Acad. Publ., 1993, vol. 407, pp. 35-55. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Hilbert modular function for \(\sqrt{5}\); periods of \(K3\) surfaces; period differential equations; theta constants Nagano, A, A theta expression of the Hilbert modular functions for \(\sqrt{5}\) via period of K3 surfaces, Kyoto J. Math., 53, 815-843, (2013) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) affine variety minus bound on the height of integral points; hyperplanes in general position; number of integral points; function fields Wang, J.T.-Y., \textit{S}-integral points of \(\mathbb{P}^n - \{2 n + 1 \text{ hyperplanes in general position} \}\) over number fields and function fields, Trans. amer. math. soc., 348, 3379-3389, (1996) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) theory of invariants; algebra of invariants; algebra of symmetric polynomials; Cohen-Macaulay rings; Gorenstein rings; groups generated by pseudoreflections; polynomial algebras L.~Smith. \textit{Polynomial invariants of finite groups}, volume~6 of \textit{Research Notes in Mathematics}. A K Peters Ltd., Wellesley, MA, 1995. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) real function fields; real holomorphy ring; valuation rings; formally real residue field; regular projective model; rational point; real prime divisors; signatures of higher level; sums of n-th powers; local-global principle; weak isotropy; quadratic forms; Henselizations Schülting, H. W.: The binary class group of the real holomorphy ring. (1986) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) cyclic trigonal Riemann surfaces; vanishings of the associated theta function; Jacobian; hyperelliptic theta functions R.D.M. Accola, \textit{On cyclic trigonal Riemann surfaces}, Trans. Amer. Math. Soc. 283 (1984) 2, 423--449. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) infinite tower of function fields; asymptotically good tower; long algebraic-geometric codes with good parameters; Artin-Schreier extensions; Kummer extensions Garcia, A.; Stichtenoth, H., Asymptotically good towers of function fields over finite fields, C. R. Acad. Sci. Paris Sér. I Math., 322, 11, 1067-1070, (1996) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) 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 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) bibliography; orthogonal reflections; regular polyhedra; Gosset; polyhedra; survey; basic invariants of reflection groups; diameter theory of algebraic surfaces; skew reflections V. F. Ignatenko, ''Some problems in the geometrical theory the invariants of groups generated by orthogonal and oblique reflections'', In:Problemy Geometrii, Vol. 16, Itogi Nauki i Tekhn., All-Union Institute for Scientific and Technical Information (VINITI), Akad. Nauk SSSR, Moscow (1984), pp. 195--229. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Anderson-Thakur function; \(L\)-functions in positive characteristic; function fields of positive characteristic Bruno Anglès & Federico Pellarin , Functional identities for \(L\) -series values in positive characteristic , J. Number Theory 142 (2014), p. 223-251 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) biholomorphic classification of ruled non-rational smooth complex projective surfaces; hyperplane section Livorni, E. L., \textit{classification of algebraic surfaces with sectional genus less than or equal six. III: ruled surfaces with dim} {\(\phi\)}\_{}\{kx\(###\)L\}, Math. Scand., 59, 9-29, (1986) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) formal languages; algebraic geometry over finite fields; rationality of zeta function; zeta function; formal power series; cyclic language; minimal ideals in finite semigroups; characteristic series; cyclic recognizable language; traces of finite deterministic automata; sofic system; symbolic dynamics J. BERSTEL and C. REUTENAUER, Zeta functions of formal languages. Trans. Amer. Math. Soc., 1990, 321, pp. 533-546. Zbl0797.68092 MR998123 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) compact Riemann surfaces; complex function fields; abelian integrals; Jacobian variety; Abel-Jacobi map \textit{Iwasawa K.}, Algebraic Functions, Amer. Math. Soc., New York and Providence (1993) (Trans. Math. Monogr.; 188). | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) noncommutative geometry; Hochshchild cohomology; Harrison cohomology; representation theory; obstruction theory; formally smooth algebras; finitely unobstructed algebras; moduli of representations A. Ardizzoni, F. Galluzzi and F. Vaccarino, A new family of algebras whose representation schemes are smooth, Ann. Inst. Fourier (Grenoble), 66 (2016), no. 3, 1261--1277. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) finite field; function field; asymptotically exact sequence; class number; tower of function fields Stéphane Ballet and Robert Rolland, Families of curves over any finite field attaining the generalized Drinfeld-Vladut bound, Actes de la Conférence ''Théorie des Nombres et Applications'', Publ. Math. Besançon Algèbre Théorie Nr., vol. 2011, Presses Univ. Franche-Comté, Besançon, 2011, pp. 5 -- 18 (English, with English and French summaries). | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) algebraic function fields; residue of differential form; system of parameters of valuation Kawahara, Y., Uchibori, T.: On residues of differential forms in algebraic function fields of two variables. TRU Math.17, 235--253 (1981) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Krichever-Novikov algebras; applications to the geometry of moduli spaces; Knizhnik-Zamolodchikov equations; second-order Casimir operators of affine Krichever-Novikov algebras; fermion representations; semi-Casimirs; tangent spaces to the moduli spaces of Riemann surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Drinfeld modules; elliptic modules; function fields; isogeny characters; torsion of Drinfeld modules | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) surface; contact of surfaces; ruled surface; enumeration | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) rank two vector bundles on algebraic surfaces; sheets; stratification of the moduli space; rational ruled surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) automorphisms; survey; Riemann surfaces; algebraic function fields; Kummer extensions | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) tensor rank; bilinear complexity; finite fields; algebraic function fields Ballet, S.: A note on the tensor rank of the multiplication in certain finite fields, Ser. number theory appl. 5, 332-342 (2008) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) finite fields; number theory; algebraic geometry; permutation polynomials; multilinear equations; quadratic forms; characters; Gauss sums; Jacobi sums; diagonal equations; zeta function; Chevalley's theorem; law of quadratic reciprocity; Davenport-Hasse theorem; Fermat curve; elliptic curve Small, C.: Arithmetic of finite fields. Monogr. textbooks pure appl. Math. 148 (1991) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) algebraic geometry; Riemann hypothesis; function fields; Severi's algebraic theory of correspondences on algebraic curves André Weil [3] On the Riemann hypothesis in function-fields , Proceedings of the National Academy of Sciences, vol. 27 (1941), pp. 345-347. Duke University. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) fields of characteristic 3; lines on quartic surfaces Rams, S.; Schütt, M., 112 lines on smooth quartic surfaces (characteristic 3), Q. J. Math., 66, 941-951, (2015) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Grothendieck group of skew-symmetric spaces; Witt group; zero-cycles; rational equivalence; real affine surface Ojanguren, M; Parimala, R; Sridharan, R, Symplectic bundles over affine surfaces, Comment. Math. Helv., 61, 491-500, (1986) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) symmetric bialgebra; skew symmetric bialgebra; bialgebra of binary forms; bialgebra of ternary forms; semisimplicity; weak semisimplicity; apolarity; Salmon subalgebra; Wiman subalgebra M. Gizatullin, ``Bialgebra and geometry of plane quartics'', Asian J. Math., 5:3 (2001), 387 -- 432 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) embeddings of algebraic surfaces in \(\mathbb{P}^ 4\); ruled surfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) \(\dagger\)-adic algebras; \(p\)-adic de Rham cohomology; \(p\)-adic de Rham complex; factorization of the zeta function; functoriality; group of automorphisms; transfer module; special module; \(p\)-adic differential operators; cohomological operations; flat liftings; \(\dagger\)-adic schemes; infinitesimal site; Gysin sequence; infinitesimal topos Arabia, A.; Mebkhout, Z., Sur le topos infinitésimal \textit{p}-adique d\(###\)un schéma lisse I, Ann. Inst. Fourier, 60, 6, 1905-2094, (2010) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) tower of function fields; number of rational places; Zink's bound | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) diophantine equations; analogue of Thue equation; polynomial ring; diophantine approximation in fields of series; rational function solutions; first order algebraic differential equations | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) regular ruled surfaces; Hilbert scheme; stable ruled surfaces; moduli of abstract ruled surfaces E. Arrondo, M. Pedreira, I. Sols, On regular and stable ruled surfaces in P3. In: \textit{Algebraic curves and projective geometry (Trento}, 1988), volume 1389 of \textit{Lecture Notes in Math.}, 1-15, Springer 1989. MR1023385 Zbl 0694.14015 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) \(S\)-units in function fields; complement of a conic and two lines; log Kodaira dimension Corvaja, Pietro; Zannier, Umberto, Some cases of Vojta's conjecture on integral points over function fields, J. Algebraic Geom., 1056-3911, 17, 2, 295\textendash 333 pp., (2008) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) elliptic curves; complex multiplication; abelian varieties; zeta function; modular functions; theta functions; periods of integrals; class fields; field of moduli of a polarized abelian variety; Hecke \(L\)-functions; periods of abelian integrals; period symbol; differential forms; polarizations Shimura, G., \textit{abelian varieties with complex multiplication and modular functions}, (1998), Princeton University Press, Princeton, NJ | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) affine group schemes; category of commutative and cocommutative Hopf algebras; counitary \(K\)-coalgebras; internal Hom; Hopf algebra maps; right adjoint functor; tensor product of Hopf algebras; monoidal closed category | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) rational function fields; moduli varieties of stable symplectic vector bundles; rationality Katsylo, PI, Birational geometry of moduli varieties of vector bundles over \({\mathbb{P}}^2\), Math. USSR-Izv., 38, 419-428, (1992) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) function fields; class group; continued fractions; generalization of Hirzebruch's theorem; class number González, CD, Class numbers of quadratic function fields and continued fractions, J. Number Theory, 40, 38-59, (1992) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) connected semisimple Lie group; flag variety; Cartan subalgebra; twisted differential operators; enveloping algebra; infinitesimal character; localization function; topological tensor product; derived categories; derived functors of localization; equivalences of categories; Harish- Chandra modules; category of representations H. Hecht and J. Taylor, Analytic localization of representations, preprint. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) rational elliptic surfaces; del Pezzo surfaces; isotrivial rational elliptic surfaces; Zariski-density of rational points on algebraic varieties; points of an elliptic curve over a function field; root number of an elliptic curve | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) 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 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) tensor rank; real tensor rank; real symmetric tensor rank; additive decomposition of polynomials; typical rank | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) error-correcting code; \(C_{ab}\) curves; towers of algebraic function fields; genus Shor, Caleb McKinley, Genus calculations for towers of functions fields arising from equations of \(C_{ab}\) curves, Albanian J. Math., 5, 1, 31-40, (2011) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) natural Lagrangian system; monoidal transformation of real analytic manifold; normal crossing; logarithmic fields; inversion of Lagrange-Dirichlet theorem; critical point; analytic potential function; Lyapunov's problem; supercritical motions; Lagrangian system with gyroscopic forces Palamodov, V.P.: Stability of motion and algebraic geometry. In: Dynamical Systems in Classical Mechanics (Amer. Math. Soc. Transl. Ser. 2), vol. 168, 5--20 (1995) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) real function fields; real holomorphy ring; valuation rings; formally real residue field; regular projective model; rational point; real prime divisors; signatures of higher level; sums of n-th powers; Local-Global- Principle; weak isotropy; quadratic forms; Henselizations SCHÜLTING, H.W.: Prime divisors on real varieties and valuation theory. J. Alg.98, 499-514 (1986) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Pieri operators; Pieri formula; graded operation; Hopf algebra; quasi-symmetric functions; skew Schur functions; generating function; skew Schubert functions; Stanley symmetric functions; poset Bergeron, Mykytiuk, Sottile, and van Willigenburg, ''Non-commutative Pieri operators on posets,'' J. Combin. Th. Ser. A 91 (2000), 84--110. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) compact Riemann surfaces; dessins d'enfants; fields of moduli; fields of definition; Shimura curves | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Hilbert scheme of smooth connected curves; regular components; ruled surfaces; double covers | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) equivalence classes; nonsingular pencils of quadratic forms of even order; hyperelliptic function fields; norm map | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) symmetric polynomial of noncommutative variables; degree; Hessian; signature; eigenvalue H. Dym, J. W. Helton and S. McCullough, The Hessian of a non-commutative polynomial has numerous negative eigenvalues, Journal d'Analyse Mathématique 102 (2007), 29--76. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Schur polynomials; isotropic Grassmannians; degeneracy loci; image of a proper morphism; desingularization; skew-symmetric morphisms Pragacz, P. Cycles of Isotropic Subspaces And Formulas For Symmetric Degeneracy Loci. Topics in algebra, Part 2 (Warsaw, 1988), Banach Center Publ., vol. 26, pp. 189--199. PWN, Warsaw (1990). | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) spacing distributions of zeros; zeros of the Riemann zeta-function; zeta functions of curves over finite fields; Montgomery-Odlyzko law; Ramanujan \(L\)-function; pair correlation; random matrix models; symplectic symmetry Katz, N.M., Sarnak, P.: Zeroes of zeta functions and symmetry. Bull. Am. Math. Soc. (N.S.) \textbf{36}(1), 1-26 (1999b) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) graded ring; graded algebras; regular rings; noncommutative analogues of polynomial algebras; noetherian; global dimension | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Hilbert function of determinantal ideals; rings with straightening law; Hodge algebras Gräbe, H.-G.: Über Streckungsringe. Beiträge zur Algebra und Geometrie 23 (1986), 85-100. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Drinfeld modular curve; expository paper; Shimura-Taniyama-Weil conjecture; function fields; rigid analytic geometry; Drinfeld modules of rank two; moduli space Gekeler ( E.U. ) and Reversat ( M. ) .- Some results on the Jacobians of Drinfeld modular curves , Preprint Univ. Toulouse 3 ( 1991 ). MR 1196521 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) cohomology theories of noncommutative operator algebras; Lie; algebra of infinite matrices of finite type; homological K-functor; \(C^*\)-algebras; Kasparov's KK-functor; cyclic homology; Gel'fand-Fuks cohomology theory of infinite-dimensional Lie; algebras; additive K-functor; derived functors; Chern characters; Bott periodicity; crystalline cohomology; differential graded algebra; de Rham complex; Gel'fand-Fuks cohomology theory of infinite-dimensional Lie algebras Feĭgin, Boris; Tsygan, Boris, Additive \(K\)-theory and crystalline cohomology, Funktsional. Anal. i Prilozhen., 19, 2, 52-62, 96, (1985) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) elliptic curves over function fields; Mordell-Weil lattices; \(L\)-function of an elliptic curve over a function field T. Shioda, Some remarks on elliptic curves over function fields , Astérisque 209 (1992), 12, 99-114. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) honeycombs; puzzles; hives; combinatorics of complex Grassmannians; additive and multiplicative Horn problems; Littlewood-Richardson coefficients; Gromov-Witten invariants; Knizhnik-Zamolodchikov equations; symmetric and affine symmetric groups; Hecke and Verlinde algebras; Kashivara crystals Veneziano | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) rational points; homogeneous polynomial; quasi-projective variety; Hilbert subset; algebraic cycle with rational coefficients; finite fields; rationality of the zeta function of Hilbert sets; Dwork's rationality theorem; decomposition theorem Wan, Daqing: Hilbert sets and zeta functions over finite fields, J. reine angew. Math. 427, 193-207 (1992) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) excellent function field; curve of genus 0; quadratic forms over function fields M. Rost, On quadratic forms isotropic over the function field of a conic, Mathematische Annalen 288 (1990), 511--513. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) 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 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) dilogarithm; \(K\)-theory of fields; hyperbolic geometry; Dedekind function; polylogarithms; motivic complexes; Zagier's conjecture; curves; regulators; special values of \(L\)-functions; motivic Lie algebra; framed mixed Tate motives; hyperlogarithms A. Goncharov, \textit{Polylogarithms in arithmetic and geometry}, \textit{Proc. ICM}\textbf{1-2} (1995) 374. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) infinite-dimensional Lie algebras; representations of the Witt algebra; symmetric polynomials; symmetric powers of curves; commuting operators; polynomial dynamical systems | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Weierstrass statement; algebraic addition theorem; meromorphic functions; Picard varieties; continuation of closed subgroup; separately extendable meromorphic functions; algebraic function fields; quasi-abelian functions; extendable line bundles on toroidal groups Abe, Y., A statement of Weierstrass on meromorphic functions which admit an algebraic addition theorem, J. Math. Soc. Jpn., 57, 709-723, 07, (2005) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) noncommutative algebras; helices; projective spaces; Fano varieties; deformations; automorphisms of two-dimensional cubic curves A. I. Bondal and A. E. Polishchuk, Homological properties of associative algebras: the method of helices, Izv. Ross. Akad. Nauk Ser. Mat. 57 (1993), no. 2, 3 -- 50 (Russian, with Russian summary); English transl., Russian Acad. Sci. Izv. Math. 42 (1994), no. 2, 219 -- 260. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) irreducible maps; bilinear forms; vector fields on spheres; multiplicities of indecomposable summands; Artin algebras S. Brenner, M.C.R. Butler, A.D. King, Irreducible maps and bilinear forms, Linear Algebra Appl., this issue | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) noncommutative projective geometry; noncommutative surfaces; Sklyanin algebras; noetherian graded rings; noncommutative blowing-up D. Rogalski, S. J. Sierra and J. T. Stafford, Classifying orders in the Sklyanin algebra, 2013.arXiv:1308.2213 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) degenerations of fibered surfaces; surface of a general type; fibration; components of the singular fiber; rational surfaces; ruled surfaces; surfaces fibered over a curve | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Beauville form; Fujiki invariant; irreducible hyperkähler manifold; locally symmetric variety of orthogonal type; period domain; Torelli theorem; modular form; cusp form; Weyl group; Zagier L-function; Cohen number; Siegel's formula V. Gritsenko, K. Hulek and G.\ K. Sankaran, Moduli spaces of irreducible symplectic manifolds, Compos. Math. 146 (2010), no. 2, 404-434. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) rationality of function fields; field of invariants; action of finite group; non ramified Brauer group; rationality problems; Noether problem D. J. Saltman, ''Multiplicative field invariants,''J. Algebra,106, 221--238 (1987). | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) graded skew Clifford algebras; noncommutative quadratic forms; rank; point modules Vancliff, M.; Veerapen, P. P., Point modules over regular graded skew Clifford algebras, Journal of Algebra, 420, 54-64, (2014) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) surfaces of type K3 over number fields; Mumford-Tate group; Mumford-Tate conjecture Tankeev, S. G., \textit{surfaces of type K3 over number fields and the Mumford-Tate conjecture}, Izv. Ross. Akad. Nauk Ser. Mat., 59, 179-206, (1995) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) surfaces of general type; Catanese-Debarre surfaces; symmetric determinantal quartics; Fano sixfolds | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) generalized polynomial identities; non-commutative algebraic geometry; solutions of polynomial equations; Free algebras; free fields; singularities of matrices; free ring; spectrum; non-commutative Nullstellensatz | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) singular curves over finite fields; rationality of the zeta function; functional equation of the zeta function; singular Riemann-Roch theorem Galindo, W. Zúñiga: Zeta functions of singular algebraic curves over finite fields. (1996) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) ruled irregular surfaces; conic bundles; ideal of a surface; Beilinson's spectral sequence; cohomology sheaf Abo, Hirotachi; Decker, Wolfram; Sasakura, Nobuo, An elliptic conic bundle in \(\mathbf{P}^4\) arising from a stable rank-\(3\) vector bundle, Math. Z., 229, 4, 725-741, (1998) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) height function; Mordell's conjecture; twisted Fermat curves; dual pairs of type II; symplectic form; unitary groups; irreducible dual reductive pairs; parabolic subgroups; non-ramified type I dual reductive pairs; irreducible admissible representations; Hecke algebras DOI: 10.1112/plms/s3-55.3.465 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) tensors; symmetric tensors; rank of tensor; symmetric rank of symmetric tensor; border ranks; best \(k\)-approximation of tensors S. Friedland, \textit{Remarks on the symmetric rank of symmetric tensors}, SIAM J. Matrix Anal. Appl., 37 (2016), pp. 320--337, . | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) semisimplicity of pure sheaves; finite ground field; Frobenius automorphism; semisimplicity of the Galois representations of function fields Lei Fu, On the semisimplicity of pure sheaves, Proc. Amer. Math. Soc. 127 (1999), no. 9, 2529 -- 2533. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) curves on torus surfaces; admissible divisor; multiplicity of the germ of the vector-function; reduced Weil number; total multiplicity of points; torus geometry; roots of a polynomial; Newton polygon Khovanskii, AG, Newton polygons, curves on torus surfaces, and the converse Weil theorem, Russ. Math. Surv., 52, 1251, (1997) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) reconstruction algebras; quivers with relations; noncommutative resolutions; CM-modules; surface singularities; Cohen-Macaulay singularities; labelled Dynkin diagrams; resolutions of singularities Wemyss, M., Reconstruction algebras of type \textit{D} (I), J. Algebra, 356, 158-194, (2012) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) modular function fields; principal congruence subgroups of prime level; algorithm; Newton polygon N. Ishida, N. Ishii, The equations for modular function fields of principal congruence subgroups of prime level. Manuscripta Math. 90 (1996), no. 3, 271-285. Zbl0871.11031 MR1397657 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) admissible groups; division algebras; function fields; Hasse principle; inverse Galois problem; Sylow subgroups Surendranath Reddy, B.; Suresh, V., Admissibility of groups over function fields of \textit{p}-adic curves, Adv. Math., 237, 316-330, (2013) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) noncommutative resolutions; quivers; dimer models; Calabi-Yau algebras; toric orders; weighted quiver polyhedra; orientable surfaces; cancellation algebras; Galois covers Bocklandt, R.: Calabi-Yau algebras and quiver polyhedra | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) matrices over ring; conditional expectation; Positivstellensätze; sums of squares; noncommutative associative algebras; algebras with involutions; Ore condition; diagonalization; quivers; path algebra; cyclic algebra; enveloping algebra of Lie algebra; path algebras; crossed product algebras; matrix polynomials; preordering; Lie algebras; Weyl algebras Savchuk, Y; Schmüdgen, K, Positivstellensätze for algebras of matrices, Linear Algebra Appl., 43, 758-788, (2012) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) toroidal compactifications of a discrete ball quotient; cusps of a discrete ball quotient; ruled surfaces with elliptic base | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) function fields; finite fields; towers of function fields; Artin-Schreier extensions of function fields | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Calogero phase spaces; coadjoint orbits; infinite dimensional Lie algebras; noncommutative symplectic geometry; varieties of representations; deformed preprojective algebras Bocklandt, R., Le Bruyn, L.: Necklace Lie algebras and noncommutative symplectic geometry. Math. Z. \textbf{240}, 141-167 (2002). arXiv:math/0010030 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) moduli spaces of curves; moduli spaces of \(K3\) surfaces; arithmetic quotients of bound symmetric domains Michela Artebani and Shigeyuki Kondō, The moduli of curves of genus six and \?3 surfaces, Trans. Amer. Math. Soc. 363 (2011), no. 3, 1445 -- 1462. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) rational and ruled surfaces; symplectic manifolds; Lefschetz fibrations; pseudo-holomorphic curves; global topological methods (à la Gromov); deformations of analytic structures Siebert, Bernd; Tian, Gang, Lectures on pseudo-holomorphic curves and the symplectic isotopy problem.Symplectic 4-manifolds and algebraic surfaces, Lecture Notes in Math. 1938, 269-341, (2008), Springer, Berlin | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) recursive towers of function fields over finite fields; elliptic modular curves | 0 |
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