Arithmetic and Geometry: Papers Dedicated to I.R. Shafarevich on the Occasion of His Sixtieth Birthday Volume I Arithmetic

Noboru Aoki, Professor Tetsuji Shioda (auth.), Michael Artin, John Tate (eds.)3764311118, 3764330007, 3764330023, 376433004X

Igor Rostislavovich Shafarevich has made outstanding contributions in number theory, algebra, and algebraic geometry. The flourishing of these fields in Moscow since World War II owes much to his influence. We hope these papers, collected for his sixtieth birthday, will indicate to him the great respect and admiration which mathematicians throughout the world have for him.

---

Table of contents :
Front Matter….Pages i-ix
Generators of the Néron-Severi Group of a Fermat Surface….Pages 1-12
p-adic Etale Cohomology….Pages 13-26
The Mordell-Weil Group of Curves of Genus 2….Pages 27-60
Number Theoretic Applications of Polynomials with Rational Coefficients Defined by Extremality Conditions….Pages 61-105
Infinite Descent on Elliptic Curves with Complex Multiplication….Pages 107-137
On the Ubiquity of “Pathology” in Products….Pages 139-153
Conjectured Diophantine Estimates on Elliptic Curves….Pages 155-171
Zeta-Functions of Varieties Over Finite Fields at s=1….Pages 173-194
Canonical Height Pairings via Biextensions….Pages 195-237
The Action of an Automorphism of C On a Shimura Variety and its Special Points….Pages 239-265
The Torelli Theorem for Ordinary K3 Surfaces over Finite Fields….Pages 267-276
Real Points on Shimura Curves….Pages 277-307
Special Automorphic Forms on PGSp 4 ….Pages 309-325
Sous-variétés d’une variété abélienne et points de torsion….Pages 327-352
Euler and the Jacobians of Elliptic Curves….Pages 353-359
Back Matter….Pages 361-365