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'' a la Greenberg and Coates.