Cycle relations in the affine grassmannian and applications to p-adic Galois representations

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• Robin Bartlett (Glasgow)
• Tuesday 23 January 2024, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Hanneke Wiersema.

The Breuil—Mézard conjecture concretely formulates the expectation that, under the Langlands correspondence, natural congruences between automorphic forms should be mirrored by congruences between Galois representations. In this talk I will explain some recent work which establishes new cases of this conjecture for crystalline representations of a ramified extension of Qp with small Hodge—Tate weights (roughly <= p/e). The approach is purely local and revolves around a comparison between moduli spaces of such representations and more explicit closed subschemes inside the affine grassmannian, constructed as degenerations of products of flag varieties. In particular, the methods also apply to moduli of Galois representations valued in more general split reductive groups than GLn.

This talk is part of the Number Theory Seminar series.

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