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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Représentations $p$-adiques et normes universelles I. Le cas cristallin
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by Bernadette Perrin-Riou PDF
J. Amer. Math. Soc. 13 (2000), 533-551 Request permission

Abstract:

Let $V$ be a crystalline $p$-adic representation of the absolute Galois group $G_K$ of an finite unramified extension $K$ of $\mathbb {Q}_p$, and let $T$ be a lattice of $V$ stable by $G_K$. We prove the following result: Let $\mathrm {Fil}^1V$ be the maximal sub-representation of $V$ with Hodge-Tate weights strictly positive and $\mathrm {Fil}^1T=T\cap \mathrm {Fil}^1V$. Then, the projective limit of $H^1_g(K(\mu _{p^n}), T)$ is equal up to torsion to the projective limit of $H^1(K(\mu _{p^n}), \mathrm {Fil} ^1T)$. So its rank over the Iwasawa algebra is $[K:\mathbb {Q}_p]\operatorname {dim}\mathrm {Fil}^1 V$.
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Additional Information
  • Bernadette Perrin-Riou
  • Affiliation: Département de Mathématiques, UMR 8628 du CNRS, bât 425, Université Paris-Sud, F-91405 Orsay Cedex, France
  • Email: bpr@geo.math.u-psud.fr
  • Received by editor(s): April 29, 1999
  • Received by editor(s) in revised form: January 10, 2000
  • Published electronically: March 13, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 13 (2000), 533-551
  • MSC (2000): Primary 11S20, 11R23, 11G25
  • DOI: https://doi.org/10.1090/S0894-0347-00-00329-5
  • MathSciNet review: 1758753