Year: 2024
Type: article
Abstract: 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 ޚ 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 ∞ /K of a p-adic field K , and compute the super-Hölder vectors in the tilt of K ∞ .We show that these super-Hölder vectors are the perfection of the field of norms of K ∞ /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 given by the endomorphisms of the corresponding Lubin-Tate group.Introduction 195 1. Super-Hölder functions and vectors 197 2. The field of norms 200 3.The Lubin-Tate case 203 4. Mahler expansions and super-Hölder functions 206 References
Source: Algebra & Number Theory
Authors: Laurent Berger, Sandra Rozensztajn
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4297612007