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Lubin-Tate generalizations of the p-adic Fourier transform

Laurent Berger

Abstract

Fresnel and de Mathan proved that the p-adic Fourier transform is surjective. We reinterpret their result in terms of analytic boundaries, and extend it beyond the cyclotomic case. We also give some applications of their result to Schneider and Teitelbaum's p-adic Fourier theory, in particular to generalized Mahler expansions and to the geometry of the character variety.

Lubin-Tate generalizations of the p-adic Fourier transform

Abstract

Fresnel and de Mathan proved that the p-adic Fourier transform is surjective. We reinterpret their result in terms of analytic boundaries, and extend it beyond the cyclotomic case. We also give some applications of their result to Schneider and Teitelbaum's p-adic Fourier theory, in particular to generalized Mahler expansions and to the geometry of the character variety.
Paper Structure (8 sections, 15 equations)

This paper contains 8 sections, 15 equations.

Table of Contents

  1. Construction of analytic boundaries
  2. $p$-adic holomorphic functions and analytic boundaries
  3. LT-like power series
  4. Construction of auxilliary functions
  5. Applications to $p$-adic Fourier theory
  6. $p$-adic Fourier theory
  7. The Peano map
  8. The character variety

Theorems & Definitions (24)

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  • ...and 14 more