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- W4301403997 abstract "We prove conjectures of Breuil and Breuil-Dembele (C. Breuil, Sur un probleme de compatibilite local-global modulo p pour GL(2)), including a generalisation from the principal series to the cuspidal case, subject to a mild global hypothesis that we make in order to apply certain R=T theorems. More precisely, we prove a multiplicity one result for the mod p cohomology of a Shimura curve at Iwahori level, and we show that certain apparently globally defined lattices in the cohomology of Shimura curves are determined by the corresponding local p-adic Galois representations. We also indicate a new proof of the Buzzard-Diamond-Jarvis conjecture in generic cases. Our main tools are the geometric Breuil-Mezard philosophy developed by two of the authors, and a new and more functorial perspective on the Taylor-Wiles-Kisin patching method. Along the way, we determine the tamely potentially Barsotti-Tate deformation rings of generic two-dimensional mod p representations, generalising a result of Breuil-Mezard in the principal series case." @default.
- W4301403997 created "2022-10-05" @default.
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- W4301403997 date "2013-05-07" @default.
- W4301403997 modified "2023-10-05" @default.
- W4301403997 title "Lattices in the cohomology of Shimura curves" @default.
- W4301403997 doi "https://doi.org/10.48550/arxiv.1305.1594" @default.
- W4301403997 hasPublicationYear "2013" @default.
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