2019/11/23 by Alexandre Pyvovarov, Pyvovarov, Alexandre
Mathematics · #Geometric and Algebraic Topology #Advanced Algebra and Geometry #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1911.10327
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.