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A de Rham weight part of Serre's conjecture and generalized mod $p$ BGG decompositions
We propose the use of de Rham cohomology of special fibers of Shimura varieties to formulate a geometric version of the weight part of Serre's conjecture. We conjecture that this formulation is equivalent to the one using Serre weights and the étale cohomology of Shimura varieties. We treat in d
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