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

This paper improves some results of the author's previous work.

We investigate the case of non-smooth points on automorphic components and prove the Breuil--Schneider conjecture under a generic Fontaine--Laffaille hypothesis on the residual Galois representation.

The residual hypothesis is formulated in terms of an extremal modular Serre weight and the maximal shape of the associated Fontaine--Laffaille module; it is the hypothesis under which weight elimination makes the relevant patched intertwining operator invertible.