Théorie d'Iwasawa des représentations cristallines II

Abstract : Let $K$ be a finite unramified extension of $\Qp$ and let $V$ be a crystalline representation of $\mathrm{Gal}(\Qpbar/K)$. In this article, we give a proof of the $C_{\mathrm{EP}}(L,V)$ conjecture for $L \subset \Qp^{\mathrm{ab}}$ as well as a proof of its equivariant version $C_{\mathrm{EP}}(L/K,V)$ for $L \subset \cup_{n=1}^\infty K(\zeta_{p^n})$. The main ingredients are the $\delta_{\Zp}(V)$ conjecture about the integrality of Perrin-Riou's exponential, which we prove using the theory of $(\phi,\Gamma)$-modules, and Iwasawa-theoretic descent techniques used to show that $\delta_{\Zp}(V)$ implies $C_{\mathrm{EP}}(L/K,V)$.
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https://hal.archives-ouvertes.fr/hal-00605387
Contributor : Laurent Berger <>
Submitted on : Friday, July 1, 2011 - 1:27:18 PM
Last modification on : Thursday, January 11, 2018 - 6:12:31 AM

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D. Benois, L. Berger. Théorie d'Iwasawa des représentations cristallines II. Commentarii Mathematici Helvetici, European Mathematical Society, 2008, 83 (3), pp.603--677. 〈hal-00605387〉

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