On the Breuil-Schneider conjecture II: Potentially crystalline non-generic case
arXiv:1911.10327
Abstract
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.
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