Super-Hölder vectors and the field of norms
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866910736402350080 |
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| author | Berger, Laurent Rozensztajn, Sandra |
| author_facet | Berger, Laurent Rozensztajn, Sandra |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2209_02572 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Super-Hölder vectors and the field of norms Berger, Laurent Rozensztajn, Sandra Number Theory 11S, 12J, 13J, 22E 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. |
| title | Super-Hölder vectors and the field of norms |
| topic | Number Theory 11S, 12J, 13J, 22E |
| url | https://arxiv.org/abs/2209.02572 |