Théorie de Sen et vecteurs localement analytiques

2014/05/21 by Berger, Laurent, Colmez, Pierre · 1 citation
#11F #11S #22E #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1405.5430

Abstract

We generalize Sen theory to extensions K_∞/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 K_∞. We describe this field in general and pay a special attention to the case of Lubin-Tate extensions.

Cited by

• Locally analytic completed cohomology of Shimura varieties of Hodge type

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• Generalization of the theory of Sen in the semi-stable representation case