On the structure of some moduli spaces of finite flat group schemes

TL;DR

This paper investigates the structure of certain moduli spaces of finite flat group schemes associated with 2-dimensional Galois representations, identifying their connected components and irreducible parts, thus confirming a modified version of Kisin's conjecture.

Contribution

It provides a detailed description of the connected and irreducible components of these moduli spaces, advancing understanding of their geometric structure.

Findings

Determined the connected components of the moduli space.

Described the irreducible components of the moduli space.

Proved a modified version of Kisin's conjecture.

Abstract

We consider the moduli space, in the sense of Kisin, of finite flat models of a 2-dimensional representation with values in a finite field of the absolute Galois group of a totally ramified extension of $mathbb{Q}_p$. We determine the connected components of this space and describe its irreducible components. These results prove a modified version of a conjecture of Kisin.