Ramification and moduli spaces of finite flat models

TL;DR

This paper investigates the structure of moduli spaces of finite flat models for 2D local Galois representations, generalizing Raynaud's theorem and analyzing zeta functions and dimensions.

Contribution

It extends Raynaud's theorem to higher ramifications and characterizes the zeta functions and dimensions of these moduli spaces.

Findings

Determined the type of zeta functions for these moduli spaces

Established the range of dimensions for the moduli spaces

Generalized Raynaud's theorem to higher ramifications

Abstract

We determine the type of the zeta functions and the range of the dimensions of the moduli spaces of finite flat models of two-dimensional local Galois representations over finite fields. This gives a generalization of Raynaud's theorem on the uniqueness of finite flat models in low ramifications.