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Article Dans Une Revue Algebra & Number Theory Année : 2024

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

Résumé

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.

Dates et versions

hal-03771463 , version 1 (07-09-2022)

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Citer

Laurent Berger, Sandra Rozensztajn. Super-H\"older vectors and the field of norms. Algebra & Number Theory, In press. ⟨hal-03771463⟩
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