Th'eorie d'Iwasawa et loi explicite de r'eciprocit'e, by Bernadette Perrin-Riou

Abstract: This paper has now appeared in Doc. Math. 4 (1999), 215-269, and so the preprint has been removed. 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 langage. 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.

Bernadette Perrin-Riou <bpr@geo.math.u-psud.fr>