Iwasawa theory and explicit reciprocity law. A remake of an article of P. Colmez

Abstract

Let $V$ be a crystalline $p$-adic representation of the absolute Galois group of ${\mathbb{Q}}_p$. The author has built the Iwasawa theory of such a representation in Invent. Math (1994) and conjectured a reciprocity law which has been proved by P. Colmez. In this text, we write the initial construction with simplification and the proof of P. Colmez in a different language. This point of view will allow us to study the universal norms in the geometric cohomology classes associated to $V$ by Bloch and Kato in a forthcoming article.