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A Deligne-Lusztig type correspondence for tame p-adic groups (49 pages, updated on 10/10/2023, arXiv:2306.02093)
We formulate a generalization of the explicit Serre weight conjectures for quasi-split tame groups.
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Heisenberg varieties and the existence of de Rham lifts (33 pages, pdf)
We show the existence of de Rham lifts for mod p L-parameters for unitary groups.
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The Emerton-Gee stacks for tame groups (66 pages, pdf)
We construct the Emerton-Gee stack for tamely ramified groups.
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The Emerton-Gee stacks for tame groups, II (37 pages, pdf)
We construct the moduli of potentially semistable Galois representations valued in tame p-adic groups and classify the irreducible components of the reduced Emerton-Gee stacks for classical groups, subject to numerical conditions which we have verified for unitary groups in the "Heisenberg variety" paper.
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Lyndon-Demushkin method and crystalline lifts of G2-valued Galois representations
(arXiv:2011.08773, submitted)
We develop the obstruction theory for lifting characteristic p Galois representations valued in reductive groups of type Bl, Cl, Dl and G2.
As an application, we show when all p > 3, all G2-valued characteristic p Galois representations admit a crystalline lift.
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Extension of Crystalline representations valued in general reductive groups.
(pdf)
We show extensions of crystalline representations valued in general reductive groups are crystalline, assuming some Hodge-Tate weights of a certain adjoint representation is slightly less than 0.
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