Geometric Methods in Algebra and Number Theory

Fedor Bogomolov, Yuri Tschinkel - Collection Progress in Mathematics

362 pages, parution le 22/03/2005

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Résumé

The transparency and power of geometric constructions has been a source of inspiration to generations of mathematicians. The beauty and persuasion of pictures, communicated in words or drawings, continues to provide the intuition and arguments for working with complicated concepts and structures of modern mathematics. This volume contains a selection of articles exploring geometric approaches to problems in algebra, algebraic geometry and number theory.

Key topics include:

Curves and their Jacobians
Algebraic surfaces
Moduli spaces, Shimura varieties
Motives and motivic integration
Number-theoretic applications, rational points
Combinatorial aspects of algebraic geometry
Quantum cohomology
Arithmetic dynamical systems

The collection gives a representative sample of problems and most recent results in algebraic and arithmetic geometry; the text can serve as an intense introduction for graduate students and those wishing to pursue research in these areas.

Contributors: I. Bauer, F. Bogomolov, N. Budur, F. Catanese, C.-L. Chai, R. Cluckers, C. De Concini, J.S. Ellenberg, F. Grunewald, B. Hassett, T. Hausel, F. Loeser, J. Pineiro, R. Pink, C. Procesi, M. Spitzweck, P. Swinnerton-Dyer, L. Szpiro, H. Tamvakis, Y. Tschinkel, T.J. Tucker, A. Venkatesh, and Y.G. Zarhin.

Sommaire

Preface
Beauville surfaces without real structures
Couniformization of curves over number fields
On the V-filtration of D-modules
Hecke orbits on Siegel modular varieties
Ax-Kochen-Ersov 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 P¹ and intersection theory on a singular arithmetic surface
A Combination of the Conjecture 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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	PAPIER
Éditeur(s)	Birkhäuser
Auteur(s)	Fedor Bogomolov, Yuri Tschinkel
Collection	Progress in Mathematics
Parution	22/03/2005
Nb. de pages	362
Format	16 x 24
Couverture	Relié
Poids	681g
Intérieur	Noir et Blanc
EAN13	9780817643492
ISBN13	978-0-8176-4349-2