Geometric methods in algebra and number theory

The transparency and power of geometric constructions has been a source of inspiration for generationsof mathematicians. Their applications to problems in algebraandnumber theory goback to Diophantus,if not earlier. Naturally, the Greek techniques of intersecting lines and conics have given way to m...

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Glavni avtor: Bogomolov, Fedor
Drugi avtorji: Tschinkel, Yuri (Éditeur intellectuel), Bogomolov, Fedor, 1946- (Directeur de la publication), Tschinkel, Yuri, 19..- (Directeur de la publication)
Format: Livre numérique
Jezik:Anglais
Izdano: Boston, MA : Birkhäuser Boston [20..].
Cham : Springer Nature
Izdaja:1st ed. 2005.
Serija:Progress in Mathematics 235
Online dostop:Accès sur la plateforme de l'éditeur
Accès sur la plateforme Istex
Accès Université d'Orléans
Accès INSA CVL
Sporočilo: Archives Springer e-books (Licence nationale)
Archives Springer e-books (Licence nationale)
Autres localisations: Voir dans le Sudoc
Edition sous un autre format:• Geometric methods in algebra and number theory, Fedor Bogomolov, Yuri Tschinkel, editors, Boston, Birkhäuser, 2005, 1 vol. (VIII-362 p.), Progress in mathematics, 0-8176-4349-4
• Geometric Methods in Algebra and Number Theory, Texte imprimé, 9780817670733
• Geometric methods in algebra and number theory, Fedor Bogomolov, Yuri Tschinkel, editors, Boston, Birkhäuser, 2005, 1 vol. (VIII-362 p.), Progress in mathematics, 0-8176-4349-4
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505 1 |a Beauville surfaces without real structures Couniformization of curves over number fields On the V-filtration of -modules Hecke orbits on Siegel modular varieties Ax-Kochen-Eršov Theorems for p-adic integrals and motivic integration Nested sets and Jeffrey-Kirwan residues Counting extensions of function fields with bounded discriminant and specified Galois group Classical and minimal models of the moduli space of curves of genus two Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve Mahler measure for dynamical systems on ?1 and intersection theory on a singular arithmetic surface A Combination of the Conjectures of Mordell-Lang and André-Oort Motivic approach to limit sheaves Counting points on cubic surfaces, II Quantum cohomology of isotropic Grassmannians Endomorphism algebras of superelliptic jacobians 
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520 |a The transparency and power of geometric constructions has been a source of inspiration for generationsof mathematicians. Their applications to problems in algebraandnumber theory goback to Diophantus,if not earlier. Naturally, the Greek techniques of intersecting lines and conics have given way to much more sophisticated and subtle constructions. What remains unchallenged is the beauty and persuasion of pictures, communicated in words or drawings. Thisvolumecontainsaselectionofarticlesexploringgeometricapproaches to problems in algebra,algebraicgeometryand number theory. All papers are strongly in?uenced by geometric ideas and intuition. Several papers focus on algebraic curves: the themes range from the study of unrami?ed curve c- ers (Bogomolov Tschinkel), Jacobians of curves (Zarhin), moduli spaces of curves (Hassett) to modern problems inspired by physics (Hausel). The - per by Bogomolov Tschinkelexplores certain special aspects of the geometry of curves over number ?elds: there exist many more nontrivial corresp- dences between such curves than between curves de?ned over larger ?elds. Zarhin studies the structure of Jacobians of cyclic covers of the projective line and provides an e?ective criterion for this Jacobian to be su?ciently generic. Hassett applies the logarithmic minimal model program to moduli spaces of curves and describes it in complete detail in genus two. Hausel st- ies Hodge-type polynomials for mixed Hodge structure on moduli spaces of representations of the fundamental groupof a complex projective curve into a reductive algebraic group. Explicit formulas are obtained by counting points over ?nite ?elds on these moduli spaces 
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