Number Theory and Algebraic Geometry

✍ Scribed by Miles Reid, Alexei Skorobogatov (eds.)

• Publisher: Cambridge University Press
• Year: 2003
• Tongue: English
• Leaves: 307
• Series: London Mathematical Society Lecture Note Series 303
• Category: Library

✦ Synopsis

Peter Swinnerton-Dyer's mathematical career encompasses more than 60 years' work of amazing creativity. This volume, dedicated to him on the occasion of his 75th birthday, provides contemporary insight into several subjects in which his influence has been notable. The contributions come from leading researchers in analytic and arithmetic number theory, and algebraic geometry. Topics treated include rational points on algebraic varieties, the Hasse principle, Shafarevich-Tate groups of elliptic curves and motives, Zagier's conjectures, descent and zero-cycles, Diophantine approximation, and Abelian and Fano varieties.

✦ Table of Contents

Cover......Page 1
Frontmatter......Page 2
Contents......Page 6
In Lieu of Birthday Greetings......Page 8
Peter Swinnerton-Dyer's mathematical papers to date......Page 30
On the Hasse principle for bielliptic surfaces......Page 38
Effective Diophantine approximation on Gm......Page 48
A Diophantine system......Page 70
Valeurs d'un polynôme à une variable représentées par une norme......Page 76
Constructing elements in Shafarevich--Tate groups of modular motives......Page 98
A counterexample to a conjecture of Selmer......Page 126
Linear relations amongst sums of two squares......Page 140
Kronecker double series and the dilogarithm......Page 184
On Shafarevich--Tate groups and the arithmetic of Fermat curves......Page 210
Cascades of projections from log del Pezzo surfaces......Page 234
On obstructions to the Hasse principle......Page 258
Abelian surfaces with odd bilevel structure......Page 286