Sur la classification de quelques phi-modules simples

TL;DR

This paper classifies simple phi-modules over a field with a semi-linear endomorphism, contributing to the understanding of finite flat group schemes in p-adic number theory.

Contribution

It provides a complete classification of simple phi-modules with semi-linear structure, extending previous work in the context of p-adic fields.

Findings

Complete classification of simple phi-modules achieved

Identification of modules involved in finite flat group schemes

Clarification of structure over Fpbar((u))

Abstract

This note is an appendix to a preprint by E. Hellmann. We give a complete classification of simple objects of the category of vector spaces D over K = Fpbar((u)) equipped with an endomorphism phi whose image generates D and that are semi-linear with respect to the ring morphism sending u to u^b (b > 1 is an integer) and acting on elements of k through a fixed automorphism. Some of these phi-modules are involved in the classification of finite flat group schemes over ring of integers of p-adic fields.