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.
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