P-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture

Recent years have witnessed significant breakthroughs in the theory of p-adic Galois representations and p-adic periods of algebraic varieties. This book contains papers presented at the Workshop on p-Adic Monodromy and the Birch and Swinnerton-Dyer Conjecture, held at Boston University in August 1991. The workshop aimed to deepen understanding of the interdependence between p-adic Hodge theory, analogues of the conjecture of Birch and Swinnerton-Dyer, p-adic uniformization theory, p-adic differential equations, and deformations of Galois representations. Much of the workshop was devoted to exploring how the special values of (p-adic and `classical') L-functions and their derivatives are relevant to arithmetic issues, as envisioned in `Birch-Swinnerton-Dyer-type conjectures', `Main Conjectures', and `Beilinson-type conjectures' à la Greenberg and Coates.

This book is a collection of papers from a workshop on this subject. The workshop aimed to deepen understanding of the interdependence between p-adic Hodge theory, analogues of the conjecture of Birch and Swinnerton-Dyer, p-adic uniformization theory, p-adic differential equations, and deformations of Galois representations.