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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2209.02572 |
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Table of Contents:
- Let E be a field of characteristic p. In a previous paper of ours, we defined and studied super-Hölder vectors in certain E-linear representations of Z_p. In the present paper, we define and study super-Hölder 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-Hölder vectors in the tilt of K_\infty. We show that these super-Hölder 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.