Arithmetic Geometry: Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, September 10-15, 2007

ISBN-13: 9783642159442 / Angielski / Miękka / 2010 / 232 str.

Jean-Louis Colliot-Thelene; Peter Swinnerton-Dyer; Paul Vojta

Opis

At the intersection of classical algebraic geometry and number theory, arithmetic geometry studies algebraic varieties through arbitrary rings. This volume collates written-up lecture notes from the 2007 ACIME summer school and covers numerous relevant topics.

Spis treści

Variétés presque rationnelles, leurs points rationnels et leurs dégénérescences.- Topics in Diophantine Equations.- Diophantine Approximation and Nevanlinna Theory.

Blurb

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.