Arithmetic Geometry

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

  • Jean-Louis Colliot-Thélène
  • Peter Swinnerton-Dyer
  • Paul Vojta
  • Pietro Corvaja
  • Carlo Gasbarri

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

Also part of the C.I.M.E. Foundation Subseries book sub series (LNMCIME, volume 2009)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Peter Swinnerton-Dyer
    Pages 45-110
  3. Back Matter
    Pages 225-232

About this book

Introduction

Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties over arbitrary rings, in particular over 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-Thélène Peter Swinnerton Dyer and Paul Vojta.

Keywords

Arithmetic Geometry Diophantine Equations Diophantine approximation Nevanlinna Theory Rationally connected varieties algebra algebraic varieties number theory

Authors and affiliations

  • Jean-Louis Colliot-Thélène
    • 1
  • Peter Swinnerton-Dyer
    • 2
  • Paul Vojta
    • 3
  1. 1.CNRS, Labo. MathématiquesUniversité Paris-Sud XIOrsay CXFrance
  2. 2., Dept. of Pure Math. & Math. StatisticsUniversity of CambridgeCambridgeUnited Kingdom
  3. 3., Department of MathematicsUniversity of California, BerkeleyBerkeleyUSA

Editors and affiliations

  • Pietro Corvaja
    • 1
  • Carlo Gasbarri
    • 2
  1. 1., Dipto. di Matematica e InformaticaUniversità di UdineUdineItaly
  2. 2.Institut de Recherche, Mathématique AvancéeUniversité de StrasbourgStrasbourgFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-15945-9
  • Copyright Information Springer-Verlag Berlin Heidelberg 2010
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-15944-2
  • Online ISBN 978-3-642-15945-9
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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