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Arithmetic Geometry

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10-15, 2007

  • Book
  • © 2010

Overview

Authors:
  1. Jean-Louis Colliot-Thélène

    1. CNRS, Labo. Mathématiques, Université Paris-Sud XI, Orsay CX, France

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  2. Peter Swinnerton-Dyer

    1. , Dept. of Pure Math. & Math. Statistics, University of Cambridge, Cambridge, United Kingdom

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  3. Paul Vojta

    1. , Department of Mathematics, University of California, Berkeley, Berkeley, USA

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Editors:
  1. Pietro Corvaja

    1. , Dipto. di Matematica e Informatica, Università di Udine, Udine, Italy

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  2. Carlo Gasbarri

    1. Institut de Recherche, Mathématique Avancée, Université de Strasbourg, Strasbourg, France

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 2009)

Part of the book sub series: C.I.M.E. Foundation Subseries (LNMCIME)

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About this book

Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties through arbitrary rings, in particular through non-algebraically closed fields. It lies at the intersection between classical algebraic geometry and number theory. A C.I.M.E. Summer School devoted to arithmetic geometry was held in Cetraro, Italy in September 2007, and presented some of the most interesting new developments in arithmetic geometry. This book collects the lecture notes which were written up by the speakers. The main topics concern diophantine equations, local-global principles, diophantine approximation and its relations to Nevanlinna theory, and rationally connected varieties. The book is divided into three parts, corresponding to the courses given by J-L Colliot-Thelene, Peter Swinnerton Dyer and Paul Vojta.

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Table of contents (3 chapters)

  1. Front Matter

    Pages i-xi
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  2. Variétés presque rationnelles, leurs points rationnels et leurs dégénérescences

    • Jean-Louis Colliot-Thélène
    Pages 1-44

  3. Topics in Diophantine Equations

    • Peter Swinnerton-Dyer
    Pages 45-110

  4. Diophantine Approximation and Nevanlinna Theory

    • Paul Vojta
    Pages 111-224

  5. Back Matter

    Pages 225-232
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Authors, Editors and Affiliations

  • , Dipto. di Matematica e Informatica, Università di Udine, Udine, Italy

    Pietro Corvaja

  • Institut de Recherche, Mathématique Avancée, Université de Strasbourg, Strasbourg, France

    Carlo Gasbarri

  • CNRS, Labo. Mathématiques, Université Paris-Sud XI, Orsay CX, France

    Jean-Louis Colliot-Thélène

  • , Dept. of Pure Math. & Math. Statistics, University of Cambridge, Cambridge, United Kingdom

    Peter Swinnerton-Dyer

  • , Department of Mathematics, University of California, Berkeley, Berkeley, USA

    Paul Vojta

Bibliographic Information

  • Book Title: Arithmetic Geometry

  • Book Subtitle: Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10-15, 2007

  • Authors: Jean-Louis Colliot-Thélène, Peter Swinnerton-Dyer, Paul Vojta

  • Editors: Pietro Corvaja, Carlo Gasbarri

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/978-3-642-15945-9

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2010

  • Softcover ISBN: 978-3-642-15944-2Published: 04 November 2010

  • eBook ISBN: 978-3-642-15945-9Published: 27 October 2010

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: XI, 232

  • Topics: Number Theory, Algebraic Geometry, Algebra

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