On the Breuil-Schneider conjecture II: Potentially crystalline non-generic case

Abstract

This paper improves some results of the author's previous work. We will investigate the case of non-smooth points on an automorphic components and prove Breuil-Schenider conjecture. As a consequence we will see that in case when all the components are automorphic in the potentially crystalline deformation rings, the Breuil-Schenider conjecture holds unconditionally.