Super-H\'older vectors and the field of norms
| Autor: | Berger, Laurent, Rozensztajn, Sandra |
|---|---|
| Rok vydání: | 2022 |
| Předmět: | |
| Zdroj: | Alg. Number Th. 19 (2025) 195-211 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.2140/ant.2025.19.195 |
| Popis: | 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. Comment: v3: minor corrections |
| Databáze: | arXiv |
| Externí odkaz: |
|