Théorie de Sen et vecteurs localement analytiques

Abstract : We generalize Sen theory to extensions $K_\infty/K$ whose Galois group is a $p$-adic Lie group of arbitrary dimension. To do so, we replace Sen's space of $K$-finite vectors by Schneider and Teitelbaum's space of locally analytic vectors. One then gets a vector space over the field of locally analytic vectors of $\hat{K}_\infty$. We describe this field in general and pay a special attention to the case of Lubin-Tate extensions.
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Contributor : Laurent Berger <>
Submitted on : Monday, May 26, 2014 - 10:50:16 AM
Last modification on : Thursday, April 4, 2019 - 10:18:05 AM

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  • HAL Id : hal-00996074, version 1
  • ARXIV : 1405.5430

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Laurent Berger, Pierre Colmez. Théorie de Sen et vecteurs localement analytiques. Annales scientifiques de l'Ecole normale supérieure, 2016, 49 (4), pp.947--970. 〈hal-00996074〉

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