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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) Castelnuovo-Mumford regularity; rational points in projective spaces over finite fields; Hilbert function; index of stability E. Kunz and R. Waldi, On the regularity of configurations of \(\mathbb{F}_q\)-rational points in projective space , J. Comm. Alg. 5 (2013), 269-280. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Humbert surfaces; transcendence properties; automorphic functions; elliptic modular function; families of abelian varieties; complex multiplication points; PEL families Paula Beazley Cohen, Humbert surfaces and transcendence properties of automorphic functions, Rocky Mountain J. Math. 26 (1996), no. 3, 987-1001. Symposium on Diophantine Problems (Boulder, CO, 1994). | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) variations of hodge structures; Toda fields; Liouville gravity; uniformization of Riemann surfaces; vector bundles | 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 of function fields; function fields over finite 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) ABC theorem in function fields; Diophantine approximation in prime characteristic; ABC theorem; truncated second main theorem; function fields of characteristic \(p\); nonvanishing result for Wronskian Julie Tzu-Yueh Wang, A note on Wronskians and the \?\?\? theorem in function fields of prime characteristic, Manuscripta Math. 98 (1999), no. 2, 255 -- 264. | 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 fibrations; elliptic \(K3\) surfaces; rational elliptic surfaces; fields of definitions of elliptic fibrations | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) framed vector bundles; ruled surfaces; instantons; moduli of vector bundles | 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 \(\wp\)-function; Mordell's theorem; Hasse's theorem; \(L\)- function; Birch and Swinnerton-Dyer conjecture; \(j\)-invariant; rational points of elliptic curves; imaginary quadratic fields; Taniyama-Weil conjecture Henri Cohen, Elliptic curves, From number theory to physics (Les Houches, 1989) Springer, Berlin, 1992, pp. 212 -- 237. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) extension of ground fields; elliptic fibration; elliptic surface; function field; conjectures of Birch and Swinnerton-Dyer G. R. Grant and E. Manduchi, Root numbers and algebraic points on elliptic surfaces with base \(\mathbbP^1\) , Duke Math. J. 89 (1997), no. 3, 413-422. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) complex conjugation; number of connected components; symmetric surfaces; real plane curves; genus; separating 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) sum of divisors function; symmetric group; permutation John R. Britnell, A formal identity involving commuting triples of permutations, J. Combin. Theory Ser. A 120 (2013), no. 4, 941 -- 943. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) deformation of complete intersection; Hilbert function; Artin algebras; peelable algebras Iarrobino, A.: Deforming complete intersection Artin algebras, appendix: Hilbert function of C[x,y]/I. Proc. sympos. Pure math. 40 (1983) | 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; equations over finite fields; arithmetic theory of algebraic curves; nonstandard arithmetic; zeta function; integral points on curves S. A. Stepanov, \textit{Arithmetic of Algebraic Curves} (Nauka, Moscow, 1991) [in Russian]. | 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 theory; valuation theory; local class field theory; algebraic number fields; algebraic function fields of one variable; Riemann-Roch theorem E. Artin, Algebraic Numbers and Algebraic Functions, Gordon and Breach, New York, 1967. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Dirichlet \(L\)-functions; moments of \(L\)-functions; function fields; finite fields; random matrix theory | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) combinatorial Hopf algebras; noncommutative symmetric functions; quasisymmetric functions; Malvenuto-Reutenauer Hopf algebras; dualities; coproducts; Grothendieck polynomials; K-theory; Schubert varieties; generating series; set-valued tableaux; Schur functions; bialgebras Lam, Thomas; Pylyavskyy, Pavlo, Combinatorial Hopf algebras and \(K\)-homology of grassmanians, Int. Math. Res. Not., 2007, 24, (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) algebraic-geometry codes; towers of function fields; \(Q\)th-power map Leonard, D. A.: Finding the missing functions for one-point AG codes. IEEE trans. Inform. theory 47, No. 6, 2566-2573 (2001) | 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 theorem; abelian category; noncommutative algebraic geometry; quasi-coherent sheaves; automorphism class group; quasi-separated scheme; the spectrum of $\mathcal A$; equivalence of groupoids; automorphism class group; derived category of coherent sheaves; tensor triangulated category of perfect complexes; Tannaka duality | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) cartography; plane trees; Belyi functions; unicellular dessin; function fields of algebraic curves N. Adrianov and G. Shabat, ''Unicellular cartography and Galois orbits of plane trees,'' in: \textit{Geometric Galois Actions}, 2, (1997), pp. 13-24. | 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 algebraic function fields; genus; number of places | 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; good reduction; regular functions; reciprocity lemma; unit; local symbols; local-global principle; solvability of diophantine equations P. Roquette, \textsl Reciprocity in valued function fields, Journal für die reine und angewandte Mathematik 375/376 (1987), 238--258. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) quiver varieties; Kac-Moody algebras; moduli space of sheaves on surfaces Schiffmann, O., Variétés carquois de Nakajima (d'après Nakajima, Lusztig, varagnolo, vasserot, crawley-boevey, et al.), Astérisque, 311, 295-344, (2008), Séminaire Bourbaki, vol. 2006/2007, Exp. No. 976 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) symmetry of cubic surfaces in Euclidean space; skew symmetry | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) coherent rings; graded algebras; noncommutative schemes; Gorenstein algebras; categories of coherent modules; coherent sheaves D. Piontkovski, Coherent algebras and noncommutative projective lines. J. Algebra 319 (2008), 3280-3290. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) differential operators; commutative affine \({\mathbb{C}}\)-algebra; coordinate ring; nonsingular affine variety; simple noetherian domain; Gelfand- Kirillov dimension; ring of invariants; group of automorphisms; simple noetherian ring; variety of symmetric n\(\times n\) matrices; simple factor ring; enveloping algebras; semisimple Lie algebras Levasseur, T.; Stafford, J. T., Rings of differential operators on classical rings of invariants, Mem. Amer. Math. Soc., 412, pp., (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) complex algebraic semisimple adjoint groups; smooth complete symmetric varieties; intersection cohomology complexes; extension algebras; derived categories; dg-algebras; categories of sheaves Guillermou, S.: Equivariant derived category of a complete symmetric variety. Represent. Theory 9, 526--577 (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) arithmetic theory of algebraic function fields; towers of function fields; Zink's bound; Hasse-Witt invariant; \(p\)-rank [2]A. Bassa and P. Beelen, The Hasse--Witt invariant in some towers of function fields over finite fields, Bull. Brazil. Math. Soc. 41 (2010), 567--582. | 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-dimensional central division algebras; rational function fields; relative Brauer groups; Picard groups DOI: 10.1016/j.jpaa.2010.06.030 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) isotropy; local-global principle; real field; sums of squares; \(u\)-invariant; pythagoras number; valuation; algebraic function fields Becher, Karim; Grimm, David; Van Geel, Jan: Sums of squares in algebraic function fields over a complete discretely valued field, Pacific J. Math. 267, No. 2, 257-276 (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) Young diagram; standard bases; symmetric tensor; skew symmetric tensor; invariant theory Rota, G.-C. \& Stein, J. A., Symbolic method in invariant theory, Proc. Natl. Acad. Sci. USA, 83 (1986), 844-847. | 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 field of elliptic curve; Witt ring; elliptic curve; generators; relations; symmetric bilinear spaces; cohomological invariants; Grothendieck ring; étale cohomology groups Arason, J. K.; Elman, R.; Jacob, B.: On the Witt ring of elliptic curves, Proc. symp. Pure math. 58, No. Part II, 1-25 (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) elliptic function; maximal-commutative algebras in the ring of differential operators; finite-gap solution | 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; genus; rational places; curves with many points A. Garcia, H. Stichtenoth, On the Galois closure of towers, preprint, 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) Galois groups of function fields; unramified cohomology; universal spaces; anabelian geometry | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) super Riemann surfaces; dressed moduli spaces; Picard group; Picard functor; Picard variety; abelian conformal field theory; vertex operator algebra; Heisenberg algebra; conformal blocks; theta functions of higher level; infinite-dimensional Lie algebras; supercurves; Beilinson-Bernstein localization; Fock representation | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) complex multiplication; \(K3\) surfaces; fields of definition; class field theory | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) unramified cohomology; Brauer groups; central division algebras; exponents; indices; smooth projective varieties; biquaternion algebras; function fields Colliot-Thélène, J.-L., Exposant et indice d'algèbres simples centrales non ramifiées, Enseign. Math. (2), 48, 1-2, 127-146, (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) Galois closure; ring extensions; algebras of finite rank; finite étale algebra; symmetric Galois group | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) scrolls; multiple coverings of ruled rational complex 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) projective complex varieties; cohomology groups; Brauer groups; function fields; quaternion algebras; biquaternion division algebras; Azumaya algebras; equivariant cohomology Andrew Kresch, Hodge-theoretic obstruction to the existence of quaternion algebras, Bull. London Math. Soc. 35 (2003), no. 1, 109 -- 116. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) polynomial automorphisms; tame automorphisms; affine spaces over finite fields; automorphism group; bijections; set of zeros; primitive subgroup of the symmetric group S. Maubach, Polynomial automorphisms over finite fields, Serdica Math. J. 27 (2001), no. 4, 343--350. | 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 algebraic function fields; genus; number of places | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) stability; vector bundle; symmetric power; ruled surface; cone of 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) covering of stable genus three curves; fibre of Prym map; abelian surface; symmetric theta divisor; Satake compactification of the moduli space of principally polarized abelian surfaces Verra, A.: The fiber of the Prym map in genus 3. Math. Ann. 276, 433--448 (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) curve over a global field; \(K_1\); local class field theory of curves; Galois cohomology; surfaces over finite fields Wayne Raskind, On \?\(_{1}\) of curves over global fields, Math. Ann. 288 (1990), no. 2, 179 -- 193. | 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 degenerations of minimal ruled surfaces; conic bundles | 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; reduced norms; function field of \(p\)-adic curves; Galois cohomology | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) first order theory of function fields in the language of fields; curves; undecidability Jean-Louis Duret, Sur la théorie élémentaire des corps de fonctions, J. Symbolic Logic 51 (1986), no. 4, 948 -- 956. | 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 geometric codes; towers 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) deformation theory; graph complexes; deformation complexes; Grothendieck-Teichmüller; Lie algebra; Operad; tensor algebras; fedosov resolution; polyvector fields; Maurer-Cartan equation; Grothendieck-Teichmüller group; twisting operads Dolgushev, V., Rogers, C.L., Willwacher, T.: Kontsevich's graph complex, GRT, and the deformation complex of the sheaf of polyvector fields (2012). arxiv:1211.4230 | 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; resolution of singularities; generating function Borisov L and Libgober A 2003 Elliptic genera of singular varieties \textit{Duke Math. J.} 116 319--51 | 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 generalizations of polynomial algebras; coordinate algebras; noncommutative differential geometry; noncommutative algebraic geometry Dubois-Violette, M.: Noncommutative coordinate algebras. In: Blanchard, E. (ed.) Quanta of Maths, dédié à à A. Connes. In: Clay Mathematics Proceedings, pp. 171--199. Clay Mathematics Institute (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) compactification of projective 3-space; singular K-3 surfaces; hypersurface isolated singularity; ruled surface; exceptional curves; Fano 3-fold . M. Furushima , Singular K3 surfaces with hypersurface singularities , Pacific J. Math. 125 (1986) 67-77. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) recursively axiomatized class; pseudo real closed fields; strongly pseudo real closed; totally transcendental; totally real; Hilbertian fields; Hilbert's irreducibility theorem; model complete; model companionable; elimination of quantifiers; decidable; orderings; Nullstellensätze; function field; holomorphy ring; Prüfer ring; generalized Jacobson ring; p-adically closed fields DOI: 10.1007/BF03322485 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) meromorphic functions; number field analogue of Nevanlinna's five-valued theorem counting multiplicities; uniqueness polynomials for complex meromorphic functions; non-Archimedean meromorphic functions; algebraic 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) semiprime graded algebras; Noetherian rings; Gelfand-Kirillov dimension; twisted homogeneous coordinate rings; Veronese rings; noncommutative projective geometry; noncommutative projective curves; algebras of quadratic growth Artin, M.; Stafford, J. T., Semiprime graded algebras of dimension two, J. Algebra, 227, 1, 68-123, (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) \(K3\) surfaces; modular invariance of complex manifolds; vanishing first Chern class; Neveu-Schwarz superalgebra; 3-folds; Calabi-Yau spaces; Jacobi function; Fermat type hypersurface; Witten's index; elliptic genus DOI: 10.1142/S0129167X92000151 | 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 rings of function fields; real analytic manifold; second residue class homomorphism; Artin-Lang property; Witt group of the ring of real analytic functions | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) tame algebras; symmetric special biserial algebras; gentle algebras; trivial extensions; Brauer graph algebras; admissible cuts; marked Riemann surfaces; triangulations Schroll, S., Trivial extensions of gentle algebras and Brauer graph algebras, J. Algebra, 444, 183-200, (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) Mordell-Weil group; procyclic extension of rational function field; elliptic curves over function fields Fastenberg, L., Mordell-Weil groups in procyclic extensions of a function field, Ph.D. Thesis, Yale University, 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) automorphism groups of affine varieties; ind-groups; Lie algebras of ind-groups; vector fields; affine \(n\)-spaces | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) \(\mu\)-stable; Grothendieck-Riemann-Roch; Donaldson polynomials; moduli space of rank two bundles on 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) Semi-stable and stable vector bundles on regular projective curves; moduli space of stable bundles; local non-abelian zeta functions for curves defined over finite fields (rationality and functional equations); global non-abelian zeta functions for curves defined over number fields; non-abelian L--functions for function fields (rationality and functional equations) Weng, L.: Non-abelian L function for number 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) transcendence of zeta values; 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) Painlevé equations; Differential algebraic function fields; analytic subgroups; algebraic subgroups; birational automorphism group of a complex algebraic variety; Pfaffian differential equations over complex manifolds; algebraic differential equations N. N. Parfentiev, ''A review on the work by Prof. Schlesinger from Giessen,'' \textit{Izvestiya Fiz.-Mat. Obshchestva pri Imperat. Kazan. Universitete}, Ser. 2, \textbf{XVIII}, 4 (1912). | 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 function; lattices; cubic polynomials; geometric realization of hyperelliptic curves; symmetric \(4p\)-gons; polynomials with nonzero discriminant; biholomorphism; Picard-Fuchs equation; hyperelliptic Riemann 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) graded algebras; global dimension; projective surfaces; noncommutative surfaces; AS-Gorenstein algebras D. Rogalski and S.J. Sierra, Some noncommutative projective surfaces of GK-dimension 4, Compos. Math. \textbf{148} (2012), 1195-1237. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) counting function; bounded height; upper bound; algebraic surface; number of rational points; nonsingular cubic surfaces; nonsingular quartic 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) formal groups; quantum groups; categories of noncommutative formal power series algebras; cogroup objects; topological Hopf algebras; quantum group law chunks Holtkamp, R.: On formal quantum group laws. Arch. math. 73, 90-103 (1999) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) efficiency of function field sieve; discrete logarithms in finite fields; supersingular elliptic curves Granger, R., Holt, A., Page, D., Smart, N.P., Vercauteren, F.: Function field sieve in Characteristic three.In: Algorithmic Number Theory Symposium - ANTS VI, pp. 223--234. Springer LNCS 3076 (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) algebraic surfaces; intersection theory; singularities; ruled surfaces; quasielliptic fibrations; minimal model theory; canonical dimension; Enriques-Kodaira classification of algebraic surfaces; characteristic \(p\); elliptic fibrations; rational surfaces Bădescu, L., Algebraic surfaces, Universitext, (2001), Springer-Verlag New York, Translated from the 1981 Romanian original by Vladimir Maşek and revised by the author. MR 1805816 | 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 powers of the Carlitz module; zeta values; motive; Tannakian category; conjectures of D. Zagier; multilogs; \(\zeta\)-functions of number fields Anderson, G.; Thakur, D., \textit{tensor powers of the Carlitz module and zeta values}, Ann. of Math. (2), 132, 159-191, (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) non-commutative deformation theory; time-space; dirac derivation; phase space; non-commutative scheme; representations of associative algebras; dynamical structure; interaction; algebraic quantum fields; connections | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) constructibility of the helices of period four; ruled rational surfaces; Markov type diophantine equations; exceptional sheaves Д. Ю. Ногин, ``Спирали периода четыре и уравнения типа Маркова'', Изв. АН СССР. Сер. матем., 54:4 (1990), 862 -- 878 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) degree of the fibre; rational fibration; 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) canonical hyperplane sections; classification of surfaces; only one effective anticanonical divisor on minimal resolution of singularities; elliptic ruled surfaces Epema, D.: Surfaces with canonical hyperplane sections, Thèse Leiden, cf. aussi: Indagationes Math.45, 173-184 (1983) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) places of algebraic function fields; description of holomorphy ring of function fields; proof of Ax-Kochen-Ershov theorem; approximation theorems Kuhlmann, F. -V.; Prestel, A.: On places of algebraic function fields. J. reine angew. Math. 353, 181-195 (1984) | 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 quasi-modular forms; Hankel determinants; function fields of positive characteristic | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Mickelsson-Faddeev cocycle; existence of string structures; bundle gerbe; quantum field theory; Atiyah-Patodi-Singer index theory; bundle of fermionic Fock spaces; gauge group action; Dixmier-Douady class; fermions in external fields; APS theorem; WZW model; Riemann surfaces; global Hamiltonian anomalies A. Alan Carey, A. Mickelsson, and M. Murray, ''Bundle gerbes applied to quantum field theory,'' hep-th/9711133. | 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. (1988). An Introduction to the Theory of the Riemann Zeta-Function. Cambridge Studies in Advanced Mathematics 14 . Cambridge: Cambridge Univ. 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) products of conjugates of generators; algorithms; Garside normal forms; quasipositivity in braid groups; plane real algebraic curves; trigonal real pseudoholomorphic curves; rational ruled surfaces S Y Orevkov, Quasipositivity problem for \(3\)-braids, Turkish J. Math. 28 (2004) 89 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) twistor spaces; slice regular functions; functions of hypercomplex variables; rational and ruled surfaces; slice-polynomial functions | 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; Siegel's theorem; integral points on affine curves; function-fields of characteristic zero José Felipe Voloch, Siegel's theorem for complex function fields, Proc. Amer. Math. Soc. 121 (1994), no. 4, 1307 -- 1308. | 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 function; tau function; Jacobians; finite-gap potentials; Korteweg-de Vries equation; Kadomtsev-Petviashvili equation; KP equation; KdV equation; integrable differential equations; theta functions of Riemann surfaces; elliptic finite-gap solutions; soliton equations --, New elliptic potentials.Acta Appl. Math., 36 (1994), 27--48. | 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; divisor class group of finite order; automorphisms; meromorphisms; addition theorems; structure of ring of meromorphisms; Riemann hypothesis | 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 of finite Chevalley groups; cohomology stability; connected split reductive group scheme; change of fields; algebra retract; elementary abelian \(\ell \)-subgroups; cohomology algebras; integral cohomology; cohomological restriction map Friedlander, E.: Multiplicative stability for the cohomology of finite Chevalley groups. Comment. Math. Helv.63, 108--113 (1988). Erratum: Comment. Math. Helv.64, 348 (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) Teichmüller modular function fields; pro-\(l\) number field towers; moduli stack of smooth projective curves; stability; braid groups Nakamura, H.; Takao, N.; Ueno, R., Some stability properties of Teichmüller modular function fields with pro-\textit{} weight structures, Math. ann., 302, 197-213, (1995), MR 96h:14041 | 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; hyper-Kähler varieties; moduli spaces of sheaves on \(K3\) surfaces; birational motives; abelian varieties; co-algebras | 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 algebra; value group; center; Brauer group; tensor products of symbol algebras; Dubrovin valuation rings; armatures; central simple algebras Adrian R. Wadsworth, Valuations on tensor products of symbol algebras, Azumaya algebras, actions, and modules (Bloomington, IN, 1990) Contemp. Math., vol. 124, Amer. Math. Soc., Providence, RI, 1992, pp. 275 -- 289. | 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; rational points; finite fields; hypergeometric functions; Deuring's polynomial Hasegawa, On asymptotically optimal towers over quadratic fields related to Gauss hypergeometric functions, Int. J. Number Theory 6 pp 989-- (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) generic matrices; stable rationality; fields of invariants; group algebras; lattices Beneish, E.: Induction Theorems on the center of the ring of generic matrices. Trans. Am. Math. Soc. 350(9), 3571--3585 (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) function fields; irreducible polynomials; hyperelliptic curves; derivatives of \(L\)-functions; moments of \(L\)-functions; quadratic Dirichlet \(L\)-functions; random matrix theory | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) linear systems of divisor on \(r\)-fold symmetric products of elliptic curves; surfaces of general type; moduli of surfaces; Kodaira-Spencer map; Kuranishi family Catanese, F.; Ciliberto, C., Symmetric products of elliptic curves and surfaces of general type with \(p_g=q=1\), J. Algebr. Geom., 2, 389-411, (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) Waring rank; symmetric tensors; homogeneous polynomials; ideals of points; Hilbert function; apolarity | 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; explicit computation of \(L\)-functions; special values of \(L\)-functions and BSD conjecture; estimates of special values; analogue of the Brauer-Siegel 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) deformation types of arbitrary ruled surfaces; no moduli scheme parametrizing all ruled surfaces with given Chern numbers 10.1515/crll.1992.426.203 | 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; Bombieri-lang conjecture; varieties of general type | 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 forms; \(u\)-invariant; power series fields; function fields of curves; orderings of fields; patching of fields Scheiderer, Claus: The u-invariant of one-dimensional function fields over real power series fields, Arch. math. (Basel) 93, No. 3, 245-251 (2009) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) class numbers; function fields; mean values of \(L\)-functions Andrade, J. C., A note on the mean value of \textit{L}-functions in function fields, Int. J. Number Theory, 8, 7, 1725-1740, (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) algebraic function fields; finite field of constants; Severi's algebraic theory of correspondences; Hurwitz's transcendental theory; group of divisor classes; Riemann hypothesis for function fields; action of Galois group André Weil, Sur les fonctions algébriques à corps de constantes fini, C. R. Acad. Sci. Paris 210 (1940), 592 -- 594 (French). | 0 |
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