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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) noncommutative tori; real multiplication; Stark numbers; real quadratic fields; spectral triples; noncommutative boundary of modular curves; modular shadows; quantum statistical mechanics | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) \(p\)-extensions of algebraic function fields; Artin-Schreier theory; characteristic \(p\); genus; number of rational points; coding theory; gap number Arnaldo Garcia and Henning Stichtenoth, Elementary abelian \(p\)-extensions of algebraic function fields, Manuscr. Math. 72 (1991), 67--79. | 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 A. S. Merkurjev, Structure of the Brauer group of fields , Izv. Akad. Nauk SSSR Ser. Mat. 49 (1985), no. 4, 828-846, 895, trad. anglaise, Math. USSR-Izv. 27 (1986), 141-157. | 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; noncommutative blowing up; Noetherian graded rings; sporadic ideals; divisor layering; graded quotient ring; twisted homogeneous coordinate ring; elliptic algebra; exceptional line modules; Godie torsion module D. Rogalski, S. J. Sierra and J. T. Stafford, Noncommutative blowups of elliptic algebras, Algebr. Represent. Theory, (2014), 1--39.Zbl 06445654 MR 3336351 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Automorphism of function fields; singular points; rational 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) rank of abelian variety; function fields; elliptic curve Pacheco, A.: The rank of abelian varieties over function fields. Manuscripta Math. 118, 361--381 (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) fields of meromorphic function; Mittag-Leffler theorem; Weierstrass theorem P. Cutillas Ripoll,Construction of certain function fields associated with a compact Riemann surface, American Journal of Mathematics106 (1984), 1423--1450. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) skew-symmetric function; determinant; decomposable; Plücker relation Duzhin, S, No article title, Decomposable skew-symmetric functions. Moscow Math. J., 3, 881-888, (2003) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Hall algebras; elliptic curves; finite fields; derived categories; flat deformations; symmetric polynomials; coherent sheaves; Drinfeld doubles I. Burban and O. Schiffmann, On the Hall algebra of an elliptic curve. I, \textit{Duke Math. J.}, 161(2012), no. 7, 1171--1231.Zbl 1286.16029 MR 2922373 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) anabelian geometry; pro-\(\ell \) groups; Galois theory; function fields; valuations theory; (Riemann) space of prime divisors; Hilbert decomposition theory; Parshin chains; decomposition graphs Pop, F., Recovering function fields from their decomposition graphs, 519-594, (2012), New York | 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 curves; algebraic function fields; maximal curves; maximal function fields; automorphisms of function fields Güneri, C.; Özdemir, M.; Stichtenoth, H., The automorphism group of the generalized giulietti-korchmáros function field, \textit{Adv. Geom.}, 13, 369-380, (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) arithmetical ruled surfaces; curves of genus 0 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) textbook; partially ordered sets; Zorn's lemma; number theory; fields; rings; abelian groups; polynomials; field extension; formal power series; polynomial rings; finite fields; power series; rational function; Bernoulli numbers; Puiseux series; Laurent series; ideals; quotient rings; factorization; Noetherian rings; prime ideals; principal ideal domains; cyclic groups; homomorphism; group action; quotient group; symmetric group; semidirect product; Sylow group; modules; free modules; commutative ring; Smith normal form; elementary divisor; Jordan form; Hermitian space; projective space; bilinear form; symplectic space; quadratic form; Kähler triples; quaternions; spinors | 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 groups; irreducible representations; Hopf algebras; Lie algebras; unipotent algebraic groups; tensor product; semisimple group representations; varieties; dimension theory of local rings; tangent spaces; Borel subgroups; Galois cohomology; automorphism groups; weights; universal enveloping algebra Hochschild, G.P.: Basic theory of algebraic groups and Lie algebras. Graduate Texts Math. \textbf{75}, (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) symmetric algebra; codimension; defect; minimal numbers of generators; Krull dimension; linear representations; algebras of invariants; symmetric and alternating groups; irreducible representations | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Mordell-Weil group; multidimensional function fields; Néron-Tate height; Mordell-Weil rank; Jacobian; independence of some rational points T. Shioda, Constructing curves with high rank via symmetry, Amer. J. Math., to appear. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Witt group of skew-symmetric non-singular bilinear forms; real algebraic variety of dimension 4; ring of \({\mathbb{C}}\)-valued regular functions; Chow ring; algebraic hypersurfaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) twisted presheaf; quasi-compact semiseparated twisted presheaf; qcss twisted presheaf; noncommutative deformation; presheaf of noncommutative algebras; deformation of abelian categories; Hochschild cohomology; Toda's construction; Gestenhaber-schack complex; deformation quantization; deformation of algebras Dinh Van, H.; Liu, L.; Lowen, W., Non-commutative deformations and quasi-coherent modules, Selecta Math., 23, 2, 1061-1119, (2016) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) X-rank; secant varieties; rank of tensor; Terracini's question; partially symmetric tensors; Comon's conjecture Buczyński, J.; Landsberg, J.M.; Ranks of tensors and a generalization of secant varieties; Linear Algebra Appl.: 2013; Volume 438 ,668-689. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) free energy; Euler characteristic of the moduli space; punctured compact Riemann surfaces; Penner's connected generating function N. Chair, Rev. Math. Phys. 3 pp 285-- (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) effective geometric Bogomolov conjecture; curves of genus 3 over function fields; self-intersection of the relative dualizing sheaf; admissible constants of the metrized dual graph K. Yamaki, Geometric Bogomolov's conjecture for curves of genus 3 over function fields, J. Math. Kyoto Univ. 42 (2002), 57-81. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Waring rank; tensor rank; symmetric tensor; sum of powers of linear forms; ternary form De Paris, A.; High-rank ternary forms of even degree; Arch. Math.: 2017; Volume 109 ,505-510. | 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; inseparable extensions of function field; Mordell conjecture for number fields; genus drop; prime characteristic; non-conservative curves Voloch, J. F.: A Diophantine problem on algebraic curves over function fields of positive characteristic. Bull. soc. Math. France 119, 121-126 (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) towers of function fields; asymptotically good towers; Drinfeld-Vladut bound; Artin-Schreier extension; long algebraic-geometric codes with good parameters García, A.; Stichtenoth, H., On the asymptotic behaviour of some towers of function fields over finite fields, J. Number Theory, 61, 248-273, (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) geometric Langlands program; Langlands correspondence for function fields; moduli stack of \(G\)-bundles; Drinfeld-Lafforgue-Vinberg compactification; singularities of the degeneration; miraculous duality of Drinfeld and Gaitsgory; Drinfeld-Wang strange invariant bilinear form S. Schieder, Picard-Lefschetz oscillators for the Drinfeld-Lafforgue-Vinberg degeneration for \(\text{SL}_{2}\), Duke Math. J. 167 (2018), 835--921. | 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 surfaces; fat points; Hilbert function DOI: 10.2478/BF02475962 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Proceedings; Symposium; Kyoto (Japan); Frobenius mappings; Commutative rings; rings with approximation property; unramified coverings; coverings of algebraic surfaces; CM modules; symbolic Rees algebras; ASL domains | 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 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 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) non-archimedean valued fields; analytic functions; \(p\)-adic cohomology; Weil conjectures; \(p\)-adic analytic varieties; action of Frobenius; rigid cohomology; \(p\)-adic analytic functions; Morita's \(p\)-adic gamma function | 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; meromorphic vector fields; theta functions; Weierstraß \(\sigma \) function M. Schlichenmaier, ''Krichever-Novikov Algebras for More Than Two Points: Explicit Generators,'' Lett. Math. Phys. 19, 327--336 (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) p-adic L-functions; CM fields; totally complex quadratic extension of a totally real field; Grössencharacter; p-adic measure; p-adic interpolation of Hecke L-function; functional equation; non-analytic Eisenstein series; Hilbert modular group; p-adic differential operators; p-adic Eisenstein series N.M. Katz, ''p-Adic L-functions for CM-fields,'' Invent. Math. 49(3), 199--297 (1978). | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Koszul complex; homomorphism of symmetric algebras; almost complete intersection; Rees ring Restuccia G.,Formes linéaires et algèbres symétriques, Bull. Sc. Math.,110 (1986), 391--410. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Clifford algebras; Euler characteristics; Quadratic fibrations; mirror symmetry; string theory; Calabi-Yau manifolds; nonlinear sigma models; Calabi-Yau manifolds; superstring theory; mirror symmetric pair; symplectic; Fukaya category; bounded derived category; Homological Projective Duality; complete intersection of quadrics; Lefshetz decomposition; non-commutative algebraic variety; Clifford non-commutative varieties; Hodge numbers; Batyrev's stringy Hodge numbers; Clifford-stringy Euler characteristics | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Sklyanin algebras; Grothendieck categories; noncommutative curves; noncommutative projective geometry; graded rings; full subcategories; categories of graded modules; Krull dimension; non-commutative schemes; quasi-schemes; quasi-coherent sheaves | 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 cycles over finite fields; zeta function; Riemann-Roch; zeta functions of zero cycles Wan, D.: Zeta functions of algebraic cycles over finite fields. Manuscripta math. 74, 413-444 (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) products of CM elliptic curves; Coleman's conjecture; endomorphism algebras; singular abelian 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) sums of squares; positive semidefinite function; formally real field; real holomorphy ring; Hilbert's 17-th problem; rational function fields; real closed field | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) tangent sheaves of generalized Raynaud surfaces; surface of general type; dimension of the space of vector fields; global differential 1-forms; cuspidal fibrations Takeda, Y.: Vector fields and differential forms on generalized raynaud surfaces. Tôhoku math. J. 44, 359-364 (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) noncommutative algebraic geometry; real spectrum; skew fields; matrix orderings; epic \(R\)-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) energy function; tensor products of Kirillov-Reshetikhin crystals T. LAM AND P.PYLYAVSKYY: Intrinsic energy is a loop Schur function, preprint, 2009; arXiv:1003.3948. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) low degree polynomial equations; complexity of the equations; Nullstellensatz; birational map; rational variety; Seiberg-Witten theory; counting function; characterization of rational surfaces; minimal models J. Kollár , 'Low degree polynomial equations: arithmetic, geometry and topology', European Congress of Mathematics I (Budapest, 1996), Progress in Mathematics 168 (Birkhäuser, Basel, 1998) 255--288. | 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; one-point code; minimum distance; Feng-Rao bound Hasegawa, T.; Kondo, S.; Kurusu, H., A sequence of one-point codes from a tower of function fields, Des. Codes Cryptogr., 41, 3, 251-267, (2006) | 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 products of symmetric powers; injective indecomposable modules; tensor products of exterior powers; tilting modules; symmetric functions; listing modules; partitions; Schur superalgebras; group schemes; representations of general linear groups; symmetric groups; Young modules Donkin, S., Symmetric and exterior powers, linear source modules and representations of Schur superalgebras, \textit{Proc. London Math. Soc.}, 83, 647-680, (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) Drinfeld modules; L-series; elliptic curve; q-expansion coefficients; Poisson kernel formula; space of cusp forms; non-archimedean measure; rigid analytic space; rigid analytic modular forms for function fields; Mellin transform J. T. Teitelbaum, The Poisson kernel for Drinfeld modular curves , J. Amer. Math. Soc. 4 (1991), no. 3, 491-511. JSTOR: | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) semisimple simply connected algebraic groups; Lie algebras; fields of formal Laurent series; Iwahori subgroups; Iwahori subalgebras; finite dimensional projective varieties; dimensions; explicit formula R. Bezrukavnikov, ''The dimension of the fixed point set on affine flag manifolds,'' Math. Res. Lett., vol. 3, iss. 2, pp. 185-189, 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) \(L\)-series of number fields; infinite-dimensional analogue of one- parameter group; Artin formalism; self-adjoint operator; associated heat kernel; characteristic kernel; trace; asymptotic expansion; regularized determinant of the Laplacian; Selberg zeta function; theta functions J. Jorgenson, S. Lang, Artin formalism and heat kernels. Jour. Reine. Angew. Math. 447 (1994), 165-280. Zbl0789.11055 MR1263173 | 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; Mordell-Weil rank; elliptic surfaces; 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) elliptic curves over function fields; Tate-Shafarevich groups; explicit computation of \(L\)-functions; BSD conjecture; Gauss and Kloosterman sums | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Markov equation for rational ruled surfaces; exceptional objects on rational ruled surfaces; rank of vector bundles; helix; mutation | 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 schemes; quantum planes; Artin-Schelter regular algebras; categories of graded right modules; finite-dimensional modules; Ore extensions; graded automorphisms; point modules Darin R. Stephenson, Quantum planes of weight (1,1,\?), J. Algebra 225 (2000), no. 1, 70 -- 92. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) skew-symmetric rank; apolarity; tensor decomposition | 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; indices; function fields of projective spaces; \(P_{n,r}\)-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) translations of classics (algebraic geometry); history of algebraic geometry; mathematics of the 19th century; algebraic functions; function fields; algebraic curves; Riemann-Roch theorem; algebraic differential 2.R. Dedekind, H. Weber, \(Theory of algebraic functions of one variable.\) Translated from the 1882 German original and with an introduction, bibliography and index by John Stillwell. History of Mathematics, 39. American Mathematical Society (Providence, RI; London Mathematical Society, London, 2012), pp. viii+152 | 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 surfaces; locally free sheaf of rank two | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) arithmetic theorem of algebraic function fields; L-function of Galois covering of curves; function-field; characteristic polynomial of the Hasse-Witt matrix; generalised Hasse-Witt invariants | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) self-dual codes; algebraic geometry codes; Gilbert-Varshamov bound; Tsfasman-Vladut-Zink bound; towers of function fields; asymptotically good codes; quadratic forms; Witt's theorem | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) operad; bar-construction; graph; symmetric function; Feynman diagram; modular operads; moduli spaces of curves; Euler characteristics; Feynman transforms E. Getzler and M. M. Kapranov, Modular operads, \textit{Compositio Math.}, 110 (1998), no. 1, 65--126.Zbl 0894.18005 MR 1601666 | 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; function field; hyperelliptic curve; moments of quadratic Dirichlet L-function; prime polynomial Andrade, J. C.; Keating, J. P., Mean value theorems for \textit{L}-functions over prime polynomials for the rational function field, Acta Arith., 161, 4, 371-385, (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) pfaffian; Azumaya algebra; quadratic form; alternating elements; discriminant module; tensor products of quaternion algebras; involution of orthogonal type; algebra with involution; involutions on central simple algebras; group of special similitudes Knus, M.-A., Parimala, R., Sridharan, R.: Pfaffians, central simple algebras and similitudes. Math. Z.206, 589-604 (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) de Rham cohomology; Dolbeault cohomology: \(N\)-point function; hybrid cohomology classes; moduli space of Riemann surfaces A. Belopolsky, \textit{New geometrical approach to superstrings}, hep-th/9703183 [INSPIRE]. | 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 ruled surfaces; space of smooth real algebraic curves; Hirzebruch surface; homotheties Jean-Yves Welschinger, Courbes algébriques réelles et courbes flexibles sur les surfaces réglées de base \Bbb C\roman\Bbb P\textonesuperior , Proc. London Math. Soc. (3) 85 (2002), no. 2, 367 -- 392 (French). | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) arithmetic quotients of Hermitian symmetric spaces; arithmetic groups; moduli varieties; Burkardt quartic threefold; cubic surfaces; parameter spaces of families of abelian varieties; quintic fourfold; automorphism group B. Hunt, \textit{The Geometry of Some Special Arithmetic Quotients}, Springer Lecture Notes in Mathematics, No. 1637, Springer--Verlag, Berlin, 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) abstract elliptic function fields; structure of ring of meromorphisms; Riemann Hypothesis Hasse, H.: Zur Theorie der abstrakten elliptischen Funktionenkörper III. Die Struktur des Meromorphismenrings. Die Riemannsche Vermutung. J. Reine Angew. Math. \textbf{175}, 193-208 (1936) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) vector bundles on a curve; ruled surfaces; moduli of vector bundles; bisecant curves; trisecant curves; Segre invariants; elementary transformation | 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 product of Riemann surfaces; Jacobian; Abel-Jacobi map; higher cohomology groups Lazarsfeld, R., Cohomology on symmetric products, syzygies of canonical curves, and a theorem of kempf, No. 145, 89-97, (1993) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) quadratic algebras; Hopf algebras; cohomology of flag manifolds; twisted group algebras; graded algebras; tensor products Fomin, S; Procesi, C, Fibered quadratic Hopf algebras related to Schubert calculus, J. Algebra, 230, 174-183, (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) symmetric products of curves; Jacobian varieties; Shafarevich conjecture implies the Mordell conjecture; zeta function; Torelli theorem J.S. Milne ; '' Jacobian varieties ''. Arithmetic geometry edited by G. Cornell, J.J. Silverman, Springer-Verlag ( 1986 ). MR 861976 | Zbl 0604.14018 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) varieties over local fields; Chow groups; algebraic \(K\)-theory; \(p\)-divisible groups; syntomic cohomology; Dieudonné modules; rings of Witt vectors; Artinian algebras Yamazaki, T.: Formal Chow groups, p-divisible groups, and syntomic cohomology. Duke math. J. 102, 359-390 (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) geometric equivalence of algebras; varieties of algebras; real-closed fields A. Berzins, ''Geometrical equivalence of algebras,''Int. J. Alg. Comput., to appear. | 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; function fields; hyperelliptic curves; \(K\)-groups; moments of quadratic Dirichlet \(L\)-functions; class number Andrade, J. C.; Bae, S.; Jung, H., Average values of \textit{L}-series for real characters in function fields, Res. Math. Sci., 3, (2016), 47 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Galois representations; Mordell-Weil lattices; elliptic curves; deformation theory of isolated singularities; Mordell-Weil group; Hasse zeta function; elliptic surfaces; Artin L-function; Weil height; del Pezzo surfaces; cubic forms Shioda, T.: Mordell-Weil lattices and Galois representation. I, II, III. Proc. Japan Acad., 65A, 269-271 ; 296-299 ; 300-303 (1989). | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) automorphism groups; cancellation problem for function fields; function fields of general type; Zariski problem | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) characteristic \(p\); \(p\)-closed rational vector fields; \(K3\) surfaces; unirational surfaces; Hirzebruch surfaces; Zariski surfaces; Enriques' surfaces; surfaces of general type; Artin invariant; quasi-elliptic surfaces M. Hirokado, Zariski surfaces as quotients of Hirzebruch surfaces by \(1\)-foliations , Yokohama Math. J., 47 (2000), 103--120. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) bounded symmetric domain; Satake compactification; theta functions; moduli space of arrangements; period space of K3 surfaces Matsumoto, K.: Theta functions on the classical bounded symmetric domain of type I2, 2. Proc. Japan Acad., Ser. A 67, 1--5 (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) Representation; uniform symmetric functions; simultaneous roots; algebraic equations; sum of products of determinants; coefficients; recurrent; function of lower order | 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 number fields; algebraic function fields; algebraic \(p\)-adic height pairing; elliptic curve; Selmer group; complex multiplication; pairing of Galois cohomology groups; Poincaré group; Galois extension | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Artin-Schreier extensions of function fields; automorphisms; \(k\)-error linear complexity; joint linear complexity; multisequences | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) explicit formulae of prime number theory; Riemann zeta-function; Poisson summation formula; Riemann hypothesis; Hadamard product formula; zeros; prime number theorem; Lindelöf hypothesis; zeta-functions attached to curves over finite fields; approximate functional equation; large number of exercises Patterson, S. J., An introduction to the theory of the Riemann zeta-function, (1995), Cambridge University Press | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) minors of multidimensional matrix; Cohen-Macaulay; Koszul algebra; Segre embedding; decomposable tensor; Hilbert function; Gröbner basis; catalecticant; ample divisor; defining ideal of blowup H.T. Hà, Box-shaped matrices and the defining ideal of certain blowup surfaces , J. Pure Appl. Alg. 167 (2001), 203-224. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) \(KP\)-equation; KdV equation; Whitham equations; completely integrable partial differential equations; abelian functions of algebraic curves; Riemann surfaces; Baker-Akhiezer function DOI: 10.1080/00036819708840541 | 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 global fields; arithmetic function fields; sheaves of differentials; Kähler differentials; arithmetic schemes; valuation rings Kunz, E.; Waldi, R.: Integral differentials of elliptic function fields. Abh. math. Sem. univ. Hamburg 74, 243-252 (2004) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) pre-spectral data for commutative subalgebras of rank 1; algebras of differential operators; Godeaux 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) isomorphism of Witt rings; Witt equivalence of fields; global field; algebraic function field Koprowski, Przemysław, Local-global principle for Witt equivalence of function fields over global fields, Colloq. Math., 91, 2, 293-302, (2002) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) twin irreducible polynomials; parity barrier over function fields; short character sums; level of distribution for irreducible polynomials | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) inverse Galois theory; Galois coverings; rigid analytic spaces; Galois 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) rational curve; formally real field; space of orderings; dense orbits property; \(Q_ 1\)-fields; function fields of real algebraic varieties; 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) quasi-symmetric algebra; symmetric algebra; Rees algebra; associated graded ring; module of derivations; module of tangent vector fields; algebraic hypersurface | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Towers of function fields; congruence function fields; genus; rational places; limits of towers; Zink's bound; cubic finite fields; Artin--Schreier extensions; Drinfeld--Vlăduţ bound; Hasse--Weil bound [4]A. Bassa, A. Garcia and H. Stichtenoth, A new tower over cubic finite fields, Moscow Math. J. 8 (2008), 401--418. | 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; 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 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) affine schemes; categories of quasicoherent sheaves; Serre's theorem; noncommutative localizations; structure sheaves; schematic algebras; noncommutative algebraic geometry; graded algebras; Ore sets; quantum groups; braided categories F. van Oystaeyen. \textit{Algebraic geometry for associative algebras}. Series ''Lect. Notes in Pure and Appl. Mathem.'' \textbf{232} (Marcel Dekker: New York, 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) Frobenius algebras; Rosenberg-Zelinsky sequence; Morita equivalences; Picard groups; categories of bimodules; monoidal categories; algebra automorphisms; exact sequences Barmeier, T.; Fuchs, J.; Runkel, I.; Schweigert, C.: On the rosenberg-zelinsky sequence in abelian monoidal categories, J. reine angew. Math. 642, 1-36 (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) surfaces of general type; canonical surfaces; canonical ring; Gorenstein algebras; canonical projections Böhning, C., Canonical surfaces \(\mathbb{P}^4\) with \(p_g = p_a = 5\) and \(K^2 = 11\), Atti Accad. Naz. Lincei Cl. Sci. Fis. Mat. Natur. Rend. Lincei (9) Mat. Appl., 18, 39-57, (2007) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) compatible systems of Galois representations; independence of algebraic monodromy groups; automorphic compatible systems; compatible systems over global 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) Polyakov string; zeta-function regularization; moduli of Riemann surfaces; Quillen metric; determinant bundle Bost, J. B.: Fibrés déterminants, déterminants régularisés et mesures sur LES espaces de modules des courbes complexes. Astérisque 152-153, 113 (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) Noncommutative symmetric systems; noncommutative symmetric functions, Azumaya algebras Zhao, W.: Noncommutative symmetric systems over associative algebras. J. pure appl. Algebra 210, No. 2, 363-382 (2007) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) dimension of linear systems of curves; Hilbert polynomial; generic Hilbert function; rational surfaces; zero-cycles B. Harbourne, \textit{The geometry of rational surfaces and Hilbert functions of points in the} \textit{plane}, in: Proceedings of the 1984 Vancouver Conference in Algebraic Geometry, CMS Conf. Proc. 6, Amer. Math. Soc., Providence, RI, 1986, 95--111. [30] B. Harbourne, \textit{Free resolutions of fat point ideals on }P2, J. Pure Appl. Algebra 125 (1998), 213--234. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) skew-symmetric matrix; globally generated vector bundle; constant rank of matrices of polynomials | 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; meromorphic vector fields; higher genus Riemann surfaces M. Schlichenmaier, ''Krichever-Novikov Algebras for More Than Two Points,'' Lett. Math. Phys. 19, 151--165 (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) multitoric surfaces; determinantal surfaces; Euler obstruction of a function; Brasselet number | 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 over number fields; diophantine equations; symmetric power of algebraic curves; Mordell conjecture; Jacobian variety; geometric gap principle; arithmetic gap priciple; gap principle for abelian varieties; quadratic point Joseph H. Silverman, Rational points on symmetric products of a curve, Amer. J. Math. 113 (1991), no. 3, 471 -- 508. | 0 |
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