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arXiv · 2209.02572

Super-H\"older vectors and the field of norms

Laurent Berger·Sandra Rozensztajn
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Abstract

Let E be a field of characteristic p. In a previous paper of ours, we defined and studied super-H\"older vectors in certain E-linear representations of Z_p. In the present paper, we define and study super-H\"older vectors in certain E-linear representations of a general p-adic Lie group. We then consider certain p-adic Lie extensions K_\infty / K of a p-adic field K, and compute the super-H\"older vectors in the tilt of K_\infty. We show that these super-H\"older vectors are the perfection of the field of norms of K_\infty / K. By specializing to the case of a Lubin-Tate extension, we are able to recover E((Y)) inside the Y-adic completion of its perfection, seen as a valued E-vector space endowed with the action of O_K^\times given by the endomorphisms of the corresponding Lubin-Tate group.

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Laurent Berger, Sandra Rozensztajn. 2022-09-06. Super-H\"older vectors and the field of norms. https://doi.org/10.2140/ant.2025.19.195

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