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Arithmetic Geometry (eBook)

Lectures given at the C.I.M.E. Summer School held in Cetraro, Italy, September 10-15, 2007
Artikelnummer: 978-3-642-15945-9
Einband: PDF
Verfügbarkeit: Download, sofort verfügbar (Link per E-Mail)
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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.

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.

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VerlagSpringer Berlin Heidelberg
EinbandPDF
Erscheinungsjahr2010
Seitenangabe232 S.
AusgabekennzeichenEnglisch
AbbildungenXI, 232 p.
Masse2'685 KB
PlattformPDF
ReiheLecture Notes in Mathematics; C.I.M.E. Foundation Subseries; Mathematics and Statistics; Mathematics and Statistics
AutorColliot-Thélène, Jean-Louis / Swinnerton-Dyer, Peter / Vojta, Paul / Corvaja, Pietro (Hrsg.) / Gasbarri, Carlo (Hrsg.)

Alle Bände der Reihe "Lecture Notes in Mathematics; C.I.M.E. Foundation Subseries; Mathematics and Statistics; Mathematics and Statistics (R0)"

Über den Autor Jean-Louis Colliot-Thélène

Jean-Louis Colliot-Thélène works in arithmetic algebraic geometry. He contributed to the study of rational points and of zero-cycles on rationally connected varieties. This involved the use of torsors and the Brauer-Manin obstruction. He applied results from algebraic K-theory (unramified cohomology) to rationality problems, also in complex algebraic geometry. He is the author of some 150 research papers, many written with various collaborators. Jean-Louis Colliot-Thélène received the Fermat prize and a Grand Prix de l'Académie des Sciences de Paris. Alexei Skorobogatov works in arithmetic algebraic geometry with focus on rational points on algebraic varieties, the Brauer group and the Brauer-Manin obstruction, K3 surfaces and abelian varieties. He is the author of the book Torsors and Rational Points and over 75 research papers. Alexei Skorobogatov is the recipient of a Whitehead prize of the London Mathematical Society.

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