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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) fusion potentials; Fibonacci numbers; cohomology ring of the Grassmannian; Schur functions; symmetric function; Waring formula; Chebyshev polynomials; Lucas numbers N. Chair, The Waring formula and fusion rings, J. Geom. Phys. 37 (2001) 216--228. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) second generalized Giulietti-Korchmáros function fields; maximal function fields; genus spectrum of maximal 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) linear groups; real curves; projective curves; function fields; strong Hasse principle; homogeneous spaces; existence of \(K\)-rational points; weak approximation; density of local points; diagonal image; central isogeny; principal homogeneous spaces; projective algebraic varieties; reciprocity law; obstruction to the Hasse principle; obstruction to weak approximation; Galois cohomology Jean-Louis Colliot-Thélène, Groupes linéaires sur les corps de fonctions de courbes réelles, J. Reine Angew. Math. 474 (1996), 139 -- 167 (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) Algebraic curves; algebraic function fields; automorphism groups of curves in positive characteristic; Stöhr-Voloch theory; curves with many points over finite fields Hirschfeld, J. W.P.; Korchmáros, G.; Torres, F., Algebraic Curves over a Finite Field, Princeton Series in Applied Mathematics, (2008), Princeton University Press: Princeton University Press Princeton, NJ, MR 2386879 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) essential dimension; essential \(2\)-dimension; central simple algebras; fields of definition; involutions; categories of field extensions; transcendence degrees; Brauer groups; cyclic algebras A. Vishik, \textit{Direct summands in the motives of quadrics}, preprint, 1999, available at http://www.maths.nott.ac.uk/personal/av/papers.html. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) categories of quasicoherent sheaves; categories of graded modules; noncommutative projective algebraic geometry; Koszul algebras; weighted projective spaces; Yoneda algebras; Auslander regular algebras; categories of torsionfree sheaves; Serre duality; almost split sequences Marti\´, R.; Villa, Nez: Serre duality for generalized Auslander regular algebras. Contemp. math. 229, 237-263 (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) algebraic-geometric codes; lattices; towers of function fields; hypergeometric analogs; theta series identities Solé, P.: Towers of function fields and iterated means. IEEE trans. Inform. theory 46, 1532-1535 (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) Morse function; regular homotopy; real algebraic surface; eversion of the sphere; closed halfway model; immersions; Boy surfaces Apéry, F.: An algebraic halfway model for the eversion of the sphere. Tohoku Math. J. 44, 103--150 (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) deforming algebras of functions; quantum groups; noncommutative spaces; categories of graded modules Vancliff M., Algebras and representation 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) algebraic function fields; arithmetic theory of correspondences | 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; 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) finite Hopf R-algebras; Azumaya algebras; rings of integers of number fields; Galois objects; smash products; Brauer group Childs, LN.: Representing classes in the Brauer group of quadratic number rings as smash products. Pacific J. Math. \textbf{129}(2), 243-255 (1987). http://projecteuclid.org/euclid.pjm/1102690574 | 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 group; inverse Galois theory; Mathieu groups; finite simple groups; embedding problems; rigidity method; Hilbertian fields; function fields; absolute Galois group; generating polynomials of Galois groups | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) global function fields; rational places; curves over finite fields; asymptotic measure of \(\mathbb{F}_q\)-rational points; class field towers; codes; Gilbert-Varshamov bound Niederreiter, H.; Xing, C., Towers of global function fields with asymptotically many rational places and an improvement on the Gilbert-varshamov bound, Math. Nachr., 195, 171-186, (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) generators; algebra of polynomial invariants; \(m\)-tuples of matrices; actions; general linear groups; class functions; reductive groups; shifted trace functions; partial tilting modules; tensor products of exterior powers; symmetric functions S. Donkin, ''Invariants of Several Matrices,'' Invent. Math. 110, 389--401 (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) central simple algebras; rational function fields; \(l\)-torsion ramification sequences; ramification indices; symbol algebras; division 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) number of rational points; cubic surfaces; Fano variety; height function Peter Swinnerton-Dyer, Counting rational points on cubic surfaces, Classification of algebraic varieties (L'Aquila, 1992) Contemp. Math., vol. 162, Amer. Math. Soc., Providence, RI, 1994, pp. 371 -- 379. | 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; algebras of invariants; algebras of symmetric polynomials; Cohen-Macaulay rings; Gorenstein rings; groups generated by pseudoreflections; polynomial 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) zeta function of several variables; simple Jordan algebra; prehomogeneous vector space; functional equations; zeta distributions; calculation of Fourier-Poisson integral; semi-simple symmetric space Blind, B.: Fonctions zeta à plusieurs variables associées aux algèbres de Jordan simples euclidiennes. C. R. Acad. sci. Paris 311, 215-217 (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) function space description of neural networks; linear network; Toeplitz matrix; circulant matrix; algebraic statistics; Euclidean distance degree; semi-algebraic set; gradient flow; discriminant; critical point; tensor | 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 stable holomorphic bundles; linear system; ruled surface; Dolgachev surfaces DOI: 10.2307/2374705 | 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; Embedded degenerations; Hilbert schemes of scrolls; Moduli A. Calabri, C. Ciliberto, F. Flamini, R. Miranda, Degenerations of scrolls to unions of planes. \textit{AttiAccad. Naz. Lincei Rend. Lincei Mat. Appl}. 17 (2006), 95-123. MR2238370 Zbl 1136.14025 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Drinfel'd twist; deformation quantization; noncommutative geometry; Hopf algebras, their representations; tangent, normal vector fields; first, second fundamental form | 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 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) current algebra; fusion rings; rational conformal field theories; cohomology of homogeneous spaces; chiral fields; chiral algebras; computation of the discriminant of a polynomial D. Gepner. ''Fusion rings and geometry''. Comm. Math. Phys. 141 (1991), pp. 381--411.DOI. | 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 Goppa codes; generalized algebraic geometry codes; code automorphisms; automorphism groups of function fields; 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) blow-up algebras; determinantal ideal; Gröbner basis; quadratic and Koszul algebra; Cohen-Macaulay algebra; liaison; vertex-decomposability; Hilbert function; Castelnuovo-Mumford regularity; Ferrers and threshold graphs; skew shapes; reductions Corso, A.; Nagel, U.; Petrović, S.; Yuen, C., Blow-up algebras, determinantal ideals, and Dedekind-mertens-like formulas, Forum Math., 29, 799-830, (2017) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Singularities; Complex analytic geometry; Proceedings; Symposium; Kyoto; RIMS; singularities in complex analytic geometry; complex affine root system; quartic surfaces of elliptic ruled type; bimeromorphic geometry of Gorenstein singularities; Torus embedding; cusp singularities; geometric genus; complex analytic foliation; Deligne, Gabber, Beilinson-Bernstein type theorem; singularities of nilpotent manifold; bifurcation set; Milnor number; quasi homogeneous polynomial; mapping singularities; Morse inequality | 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; elliptic surfaces; function fields; rank; Mordell-Weil groups; Selmer groups; Galois representations Ellenberg, J.: Selmer groups and Mordell--Weil groups of elliptic curves over towers of function fields. Compos. Math. 142, 1215--1230 (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) anisotropic quadratic forms; function fields of quadrics; Chow groups Karpenko, N., \textit{on the first Witt index of quadratic forms}, Invent. Math., 153, 455-462, (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) algebraic surfaces; Rational and ruled surfaces; compact Kähler manifolds; surfaces isogenous to a product; Lie groups of automorphisms; minimal and not minimal surfaces; cohomologically trivial; (cohomologically) rigidified; topologically trivial automorphisms; Enriques-Kodaira classification | 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 Hopf-Galois extensions; Hopf algebras; symmetric monoidal categories; noncommutative principal fibre bundles; differential graded vector spaces; differential graded algebras; differential graded algebra extensions Schauenburg, Galois type extensions of noncommutative 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) noncommutative projective schemes; noncommutative graded algebras; projective spectrum; quasi-coherent sheaves; quotient category; cohomology of coherent sheaves; cohomological dimension M. Artin and J. J. Zhang, ''Noncommutative Projective Schemes,'' Adv. Math. 109 (2), 228--287 (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) K3 surface over a finite field; Tate's conjecture on algebraic cycles; order of pole of zeta function; crystalline deformation theory; quasi-canonical varieties over p-adic fields; equicharacteristic deformations of abstract F-crystals Nygaard, Niels; Ogus, Arthur, Tate's conjecture for \(K3\) surfaces of finite height, Ann. of Math. (2), 0003-486X, 122, 3, 461-507, (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) noncommutative algebra; minimal model program; threefold flopping contractions; simultaneous resolution of singularities; Kleinian singularities; contraction 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) high tensor rank; symmetric tensor rank; zero-dimensional schemes; cactus varieties; projections 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) rational points over complex function fields; rationally connected manifolds; special manifolds; manifolds 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) Brauer groups; curves over local fields; \(p\)-adic curves; field extensions; resolutions of singularities; algebraic function fields; curves over rings of integers of \(p\)-adic fields Saltman, D. J., Division algebras over \(p\)-adic curves, J. Ramanujan Math. Soc., 12, 25-47, (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) absolute Galois groups; function fields of one variable; anabelian geometry F. Pop, ''On Grothendieck's conjecture of birational anabelian geometry,'' Ann. of Math., vol. 139, iss. 1, pp. 145-182, 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) quadric; function field of a quadric; Chow group; algebraic cobordism; symmetric operation; Landweber-Novikov operation; rationality Vishik, A., Rationality of integral cycles, Doc. Math., 661-670, (2010), Extra Volume Suslin | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Castelnuovo bound; dimension of a family of ruled surfaces; irregularity; ruled surfaces; curve in the grassmannian Eisenbud, D., Harris, J.: Curves in Projective Space. Sém. Math. Sup. \(85\) Les Presses de l'Université de Montréal (1982) | 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; finite field; Artin-Schreier extension A. Garciaand H. Stichtenoth. Some Artin-Schreier towers are easy. Mosc.Math. J., 5 (2005), 767--774. | 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 A. Garcia and H. Stichtenoth, Explicit towers of function fields over finite fields, In Topics in geometry, coding theory and cryptography , volume 6 of Algebr. Appl. , pages 1-58, Springer, Dordrecht, 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) Hilbert scheme of points; Nakajima operators; Ext-groups; Nekrasov instanton partition function; Jack symmetric functions E. Carlsson and A. Okounkov, \textit{Exts and Vertex Operators}, arXiv:0801.2565. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) genus; towers of function fields; asymptotically bad towers | 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. Bezerra, J.; Garcia, A.; Stichtenoth, H.: An explicit tower of function fields over cubic finite fields and Zink's lower bound for \(A(q3)\). J. reine angew. Math. 589, 159-199 (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 over function fields; arithmetic of algebraic curves; Mordell Weil theorem; Mordell conjecture | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) topology of real algebraic curves; Viro method; patchworking; rational ruled surfaces; pseudoholomorphic 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) Brauer groups; curves over local fields; field extensions; resolutions of singularities; algebraic function fields; curves over rings of integers of \(p\)-adic fields D. J. Saltman, ''Correction to: ``Division algebras over \(p\)-adic curves'' [J. Ramanujan Math. Soc. 12 (1997), no. 1, 25-47; MR1462850 (98d:16032)],'' J. Ramanujan Math. Soc., vol. 13, iss. 2, pp. 125-129, 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) towers of function fields; Jacobian; rank of a Jacobian; endomorphisms of Jacobians; function field D. Ulmer and Y.G. Zarhin. Ranks of Jacobians in towers of function fields. Math. Res. Lett., 17:637--645, 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) function fields; 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) Bairstow's symmetric function; algebraic descent; arithmetic descent; diophantine equations; comparison of algebraic norms | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Kazhdan-Lusztig polynomials; Schubert varieties; representations of semisimple Lie algebras; Weyl groups; symmetric groups; flag varieties; semisimple groups; torus actions \beginbarticle \bauthor\binitsS. C. \bsnmBilley and \bauthor\binitsT. \bsnmBraden, \batitleLower bounds for Kazhdan-Lusztig polynomials from patterns, \bjtitleTransform. Groups \bvolume8 (\byear2003), no. \bissue4, page 321-\blpage332. \endbarticle \OrigBibText Sara C. Billey and Tom Braden, Lower bounds for Kazhdan-Lusztig polynomials from patterns , Transform. Groups 8 (2003), no. 4, 321-332. \endOrigBibText \bptokstructpyb \endbibitem | 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 simple algebras; index changes under field extensions; function fields; homogeneous varieties; reductive algebraic groups Merkurjev, A.: Degree formula. Available at http://www.mathematik.uni-bielefeld.de/rost/degree-formula.html | 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; BSD conjecture; unbounded ranks; explicit Jacobi 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) complex reflection groups; Demazure operators; symmetric algebras; algebras of coinvariants Rampetas, K.; Shoji, T.: Length functions and Demazure operators for \(G(e,1,n)\) II, Indag. math. (N.S.) 9, No. 4, 581-594 (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) finite fields; recursive towers of function fields; generating function of the Franel 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) smooth projective varieties; flag varieties; Miyaoka's semipositivity theorem; cotangent bundle; rational surfaces; divisorial contractions; fibrations; crystalline differential operators; étale fundamental group; semistability; reflexives sheaves; semipositive sheaves; uniruled varieties; Riemann-Hilbert correspondence; stable Higgs bundle; Chern classes; flat connections; Artin's criterion of contractibility; Kodaira dimension; Hirzebruch surface; canonical divisor; surfaces of general type; Barlow's surfaces; del Pezzo surfaces; Fano three-folds | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Symmetries of surfaces Gromadzki G.: On Singerman symmetries of a class of Belyi Riemann surfaces. J. Pure Appl. Algebra 213, 1905--1910 (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) homological mirror symmetry; derived category; Del Pezzo surfaces; Landau-Ginzburg model; Lagrangian vanishing cycles; noncommutative deformations D. Auroux, L. Katzarkov, and D. Orlov, ''Mirror Symmetry for Del Pezzo Surfaces: Vanishing Cycles and Coherent Sheaves,'' Invent. Math. 166(3), 537--582 (2006); arXiv:math/0506166. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) minimal complex surfaces of general type; generic vanishing theorems Hacon, CD; Pardini, R, Surfaces with \(pg = q = 3\), Trans. Am. Math. Soc., 354, 2631-2638, (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) \(\mathcal{S}_5\)-covers; canonical resolution; surfaces of general type with positive indices; Galois closure curves; Galois points | 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 function along a subspace; implicit differentiation; formal power series; standard basis of a local ideal; resolution of singularities Edward Bierstone and Pierre D. Milman, Standard basis along a Samuel stratum, and implicit differentiation, The Arnoldfest (Toronto, ON, 1997) Fields Inst. Commun., vol. 24, Amer. Math. Soc., Providence, RI, 1999, pp. 81 -- 113. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) forms over number fields; Hasse principle; affine variety; Hardy-Littlewood circle method; asymptotic formula; number of solutions; weak approximation C.\ M. Skinner, Forms over number fields and weak approximation, Compos. Math. 106 (1997), 11-29. | 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; affine-ruled surfaces; weighted projective planes; locally nilpotent derivations; additive group actions on affine \(3\)-space | 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 Riemann surface; complex curve; groups of automorphisms G. Gromadzki. Symmetries of Riemann surfaces from a combinatorial point of view. London Mathematical Society Lecture Note Series, Cambridge University Press 287 (2001), 91--112. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) loxodromes; surfaces of revolution | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) determinantal variety; skew-symmetric matrices; linear code; minimum distance | 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; infinitesimal Torelli theorem; mixed Hodge structure | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) period map; set of isomorphy classes of Enriques surfaces; Nikulin lattice theory; existence of smooth rational curves Y. Namikawa, ''Periods of Enriques surfaces'',Math. Ann.,270, 201--222 (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) geometry of surfaces; tangential singularities; swallowtail; parabolic curve; flecnodal curve; cusp of Gauss; godron; wave front; Legendrian singularities R. Uribe-Vargas, ''A Projective Invariant for Swallowtails and Godrons, and Global Theorems on the Flecnodal Curve,'' Moscow Math. J. 6, 731--768 (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) modular curves; classification of Hilbert modular surfaces Bassendowski, D.: Klassifikation Hilbertscher Modulflächen zur symmetrischen Hurwitz-Maass-Erweiterung. Dissertation, Bonn, 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) quadratic space; conic bundle surface; resolution of singularities; orders in quaternion 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) analytic superspaces; GAGA; Chow's lemma; families of compact super Riemann surfaces Rabin, J. M.; Topiwala, P.: Super Riemann surfaces are algebraic curves. (1988) | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) set theoretic complete intersection curves; monoidal surfaces of degree 4 | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) decidability; Hilbert's Tenth Problem; uncomputably large integral points on algebraic curves; diophantine prefix; polynomials; height bounds; geometry of complex surfaces and 3-folds J.M. Rojas, Uncomputably large integral points on algebraic plane curves?, Theoret. Comput. Sci., 235 (this Vol.) (2000) 145--162. | 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 fourth and fifth degree; singularities | 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 with complex multiplication; curves of genus 2; Jacobians; product surfaces; abelian variety; Humbert invariant; binary and ternary quadratic forms; idoneal numbers; mass formula Kani, E., Jacobians isomorphic to a product of two elliptic curves and ternary quadratic forms, J. Number Theory, 139, 138-174, (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) function field of positive characteristic; arithmetic fundamental group; Galois representation; automorphic representation G. Böckle and C. Khare, Finiteness results for mod \(l\) Galois representations over 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) locally symmetric varieties; compactifications; modular forms; \(K3\) surfaces Loo E. Looijenga, \emph Compactifications defined by arrangements II: locally symmetric varieties of type IV. Duke Math. J. \textbf 119 (2003), no. 3, 527--588 (see also arXiv:math/0201218). | 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 \(K3\) surfaces; \(K3\) surfaces; lattice theory; singular \(K3\) 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) inverse Galois problem; canonical form; linear automorphisms; monomial automorphisms; fields of rational functions; survey Hajja, M.: Linear and monomial automorphisms of fields of rational functions: some elementary issues, Algebra and number theory (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) finiteness of fundamental groups of open rational surfaces; fiber of morphism Gurjar, R.V., Zhang, D.-Q.: On the fundamental groups of some open rational surfaces. Math. Ann. 306, 15--30 (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) Igusa function; moduli space; Eisenstein series; abelian surfaces Bröker, R.; Lauter, K.: Evaluating igusa functions. Math. comp. 83, 2977-2999 (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) Determinants; algebra; geometry; discussion of an equation of second degree; homogeneous coordinates; analytic criteria; plane sections of \(2^{\text{nd}}\) order surfaces; invariants of quadratic forms; plane curves of third 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) degeneracy locus; Buchsbaum subvarieties of codimension 2; moduli spaces of K3 surfaces; unirational three-folds [C] Chang M.C.: Classification of Buchsbaum subvarieties of codimension 2 in projective space. J. reine angew. Math.401, 101--112 (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) elliptic curves; modular forms; \(p\)-adic cohomology; zeta function; elliptic 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) degeneration of Riemann surfaces; topological monodromy; pseudo-periodic homeomorphism | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) Kronecker series; \(L\)-functions of symmetric powers of elliptic curves; Beilinson's conjecture; motivic cohomology groups; Bloch-Beilinson regulator; de Rham cohomology Mestre, J. -F.; Schappacher, N.: Séries de Kronecker et fonctions L des puissances symétriques de courbes elliptiques sur Q. Progr. math. 89, 209-245 (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) abelian varieties over arithmetic ground fields; moduli of abelian varities; Dieudonné 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) domain of periods; Torelli theorem; Kählerian K 3 surfaces; Hodge isometry; marked K 3 surface A. Beauville, Préliminaires sur les périodes des surfaces K3 , Astérisque 126 (1985), 91-97. | 0 |
noncommutative symmetric algebras; bimodules; tensor algebras; skew fields of frractions; function fields; noncommutative ruled surfaces Patrick D., J. Algebra 233 pp 16-- (2000) third moment of Kloosterman sums; number of rational points on smooth projective 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) \(K3\) surfaces; modular forms on symmetric 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) Moduli space; Riemann surface; Fuchsian group; strata of Riemann surfaces Costa, A. F., Izquierdo, M.: Equisymmetric strata of the singular locus of the moduli space of Riemann surfaces of genus 4. In: Geometry of Riemann surfaces, London Math. Soc. Lecture Note Ser., 368, Cambridge Univ. Press, Cambridge, 2010, 120--138 | 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 rational function field over complex 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) arithmetic zeta functions; foliated space; \(L\)-functions of 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) multilinear algebra; tensor calculus; computational aspects of algebraic; algebraic 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) equivariant compactification; symmetric varieties; character sheaves; finite groups of Lie 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) diagonal equations; cyclotomic classes; cyclotomic numbers; number of points on finite diagonal curves; 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) quotient of complex surface under the action of automorphism group; Enriques surfaces Mukai, [Mukai and Namikawa 84] S.; Namikawa, Y., Automorphisms of Enriques surfaces which act trivially on the cohomology groups., \textit{Invent. Math.}, 77, 383-397, (1984) | 0 |
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