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arXiv · 1405.5430

Théorie de Sen et vecteurs localement analytiques

Laurent Berger·Pierre Colmez
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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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Laurent Berger, Pierre Colmez. 2014-05-21. Théorie de Sen et vecteurs localement analytiques. https://arxiv.org/abs/1405.5430

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