Rational Points on Algebraic Varieties

✍ Scribed by Carmen Laura Basile, Thomas Anthony Fisher (auth.), Emmanuel Peyre, Yuri Tschinkel (eds.)

• Publisher: Birkhäuser Basel
• Year: 2001
• Tongue: English
• Leaves: 454
• Series: Progress in Mathematics 199
• Edition: 1
• Category: Library

✦ Synopsis

This book is devoted to the study of rational and integral points on higher-dimensional algebraic varieties. It contains carefully selected research papers addressing the arithmetic geometry of varieties which are not of general type, with an emphasis on how rational points are distributed with respect to the classical, Zariski and adelic topologies. The present volume gives a glimpse of the state of the art of this rapidly expanding domain in arithmetic geometry. The techniques involve explicit geometric constructions, ideas from the minimal model program in algebraic geometry as well as analytic number theory and harmonic analysis on adelic groups.

✦ Table of Contents

Front Matter....Pages i-xvi
Diagonal Cubic Equations in four Variables with Prime Coefficients....Pages 1-12
Rational Points On Cubic Surfaces....Pages 13-35
Torseurs Arithmétiques Et Espaces Fibres....Pages 37-70
Fonctions ZÊta Des Hauteurs Des Espaces Fibrés....Pages 71-115
Hasse principle for pencils of curves of genus one whose jacobians have a rational 2-division point....Pages 117-161
Enriques surfaces with a dense set of rational points....Pages 163-168
Density of Integral Points on Algebraic Varieties....Pages 169-197
Composition of Points and the Mordell—Weil Problem for Cubic Surfaces....Pages 199-219
Torseurs Universels Et Méthode Du Cercle....Pages 221-274
Tamagawa Numbers of Diagonal Cubic Surfaces of Higher Rank....Pages 275-305
The Hasse Principle for Complete Intersections in Projective Space....Pages 307-311
Une construction de courbes k -rationnelles sur les surfaces de kummer d’un produit de courbes de genre 1.....Pages 313-334
Arithmetic Stratifications and Partial Eisenstein Series....Pages 335-355
Weak Approximation and R -Equivalence on Cubic Surfaces....Pages 357-404
Hua’s Lemma and Exponential Sums over Binary Forms....Pages 405-446

✦ Subjects

Mathematics, general