Fedor Bogomolov / Yuri Tschinkel (eds.)

Geometric Methods in Algebra and Number Theory

Herausgegeben:Bogomolov, Fedor; Tschinkel, Yuri

• Gebundenes Buch

Produktbeschreibung

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-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.

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Produktdetails

• Progress in Mathematics 235
• Verlag: Birkhäuser / Birkhäuser Boston / Springer, Basel
• Artikelnr. des Verlages: 10987025, 978-0-8176-4349-2
• 2005
• Seitenzahl: 362
• Erscheinungstermin: 12. November 2004
• Englisch
• Abmessung: 236mm x 163mm x 23mm
• Gewicht: 685g
• ISBN-13: 9780817643492
• ISBN-10: 0817643494
• Artikelnr.: 13715441

Autorenporträt

Fedor Bogomolov, New York University, NY, USA / Yuri Tschinkel, Georg-August-Universität, Göttingen, Germany; and Princeton University, Princeton, NJ, USA

Inhaltsangabe

Preface Bauer/Catanese/Grunewald: Beauville surfaces without real structures Bogomolov/Tschinkel: Couniformization of curves over number fields Budur: On the V-filtration of D-modules Chai: Hecke orbits on Siegel modular varieties Cluckers/Loeser: Ax Kochen Er ov Theorems for p-adic integrals and motivic integration De Concini/Procesi: Nested sets and Jeffrey Kirwan residues Ellenberg/Venkatesh: Counting extensions of function fields with bounded discriminant and specified Galois group Hassett: Classical and minimal models of the moduli space of curves of genus two Hausel: Mirror symmetry and Langlands duality in the non-Abelian Hodge theory of a curve Pineiro/Szpiro/Tucker: Mahler measure for dynamical systems on P1 and intersection theory on a singular arithmetic surface Pink: A Combination of the Conjecture of Mordell Lang and André Oort Spitzweck: Motivic approach to limit sheaves Swinnerton-Dyer: Counting points on cubic surfaces, II Tamvakis: Quantum cohomology of isotropic Grassmannians Zarhin: Endomorphism algebras of superelliptic Jacobians

Rezensionen

From the reviews: "This is a collection of articles on algebraic and arithmetic geometry most of which were presented at a conference that took place in Miami in December 2003. ... this volume will be attractive for researchers and graduate students in arithmetic geometry. The surveys provided can serve as an introduction for them and offer guidance for further study." (Ch. Baxa, Monatshefte für Mathematik, Vol. 152 (1), September, 2007)