A Harder-Narasimhan theory for Kisin modules
  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. 
Brandon Levin, Carl Wang-Erickson
math.NT math.AG