A Harder-Narasimhan theory for Kisin modules

TL;DR

This paper extends the Harder-Narasimhan theory to Kisin modules, proving a tensor product theorem and applying it to Kisin varieties for connected reductive groups.

Contribution

It generalizes the Harder-Narasimhan theory to Kisin modules and establishes the tensor product theorem for semi-stable objects.

Findings

Tensor product of semi-stable Kisin modules remains semi-stable

Application of the theory to Kisin varieties for connected reductive groups

Development of a generalized Harder-Narasimhan framework

Abstract

We develop a Harder-Narasimhan theory for Kisin modules generalizing a similar theory for finite flat group schemes due to Fargues. We prove the tensor product theorem, i.e., that the tensor product of semi-stable objects is again semi-stable. We then apply the tensor product theorem to the study of Kisin varieties for arbitrary connected reductive groups.