DOCUMENTA MATHEMATICA, Vol. 4 (1999), 219-273

Bernadette Perrin-Riou

Théorie d'Iwasawa et Loi Explicite de Réciprocité

Let $V$ be a crystalline $p$-adic representation of the absolute Galois group of $\Q_p$. 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.

1991 Mathematics Subject Classification: 11E95 11R23

Keywords and Phrases: $p$-adic representation, Iwasawa theory, exponential, reciprocity law

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