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Geometric methods in algebra and number theory

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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,  Read more...

Abstract: 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 surfaceModuli spaces, Shimura varieties- Motives and motivic integration- Number-the

Author(s): Bogomolov, Fedor; Tschinkel, Yuri (eds.)
Publisher: Birkhauser;Springer
Year: 2005

Language: English
Pages: 364
City: Dordrecht
Tags: Algebra.;Geometry, Algebraic.;Number theory.;Mathematics.;Algebraic Geometry.;Number Theory.;Geometry.

Content: 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.