Th\'eorie d'Iwasawa des repr\'esentations cristallines II

Publication date: 27 September 2005

Abstract: Let

K

be a finite unramified extension of

Q p

and let

V

be a crystalline representation of

m a t h r m G a l (Q p b a r / K)

. In this article, we give a proof of the

C_{m a t h r m E P} (L, V)

conjecture for

L s u b s e t Q p^{m a t h r m a b}

as well as a proof of its equivariant version

C_{m a t h r m E P} (L / K, V)

for

L s u b s e t c u p_{n = 1}^{i} n f t y K (z e t a_{p^{n}})

. The main ingredients are the

conjecture about the integrality of Perrin-Riou's exponential, which we prove using the theory of

(p h i, G a m m a)

-modules, and Iwasawa-theoretic descent techniques used to show that

implies

C_{m a t h r m E P} (L / K, V)

.

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