Estimation des dimensions de certaines vari\'et\'es de Kisin

TL;DR

This paper estimates the dimensions of certain Kisin varieties related to Galois representations, providing specific results for a special case and proposing a conjecture for the general case.

Contribution

It offers a dimension estimation for a special case of Kisin varieties and formulates a conjecture for the broader case.

Findings

Dimension bounds for a special case of Kisin varieties

A conjecture for the dimension in the general case

Foundation for future research on Galois representation varieties

Abstract

In this paper, we study dimensions of some varieties, that were introduced recently by Kisin in order to prove modularity of some Galois representations. In fact, we mainly consider a special case for which we obtain an estimation of the dimension we are interested in. Then, based on this result, we state a conjecture for the general case.