Under standard assumptions the GK-dimension of Hecke eigenspaces in mod p cohomology of D^x for inner forms D of GL2 over totally real fields unramified at p is computed, including the division-algebra-at-p case, and the same arguments simplify a prior theorem for the matrix-algebra case.
215, Princeton University Press, Princeton, NJ, [2023] 2023
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A partial resolution of crystalline Galois representation spaces proves automorphy lifting, the weight part of Serre's conjecture, and the Breuil-Mézard conjecture in dimension three for minimal regular weight.
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Gelfand--Kirillov dimension and mod $p$ cohomology for inner forms of $\mathrm{GL}_2$
Under standard assumptions the GK-dimension of Hecke eigenspaces in mod p cohomology of D^x for inner forms D of GL2 over totally real fields unramified at p is computed, including the division-algebra-at-p case, and the same arguments simplify a prior theorem for the matrix-algebra case.
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Resolutions of spaces of crystalline representations and modularity
A partial resolution of crystalline Galois representation spaces proves automorphy lifting, the weight part of Serre's conjecture, and the Breuil-Mézard conjecture in dimension three for minimal regular weight.