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SUMMARY:Cycle relations in the affine grassmannian and applications to p-a
 dic Galois representations - Robin Bartlett (Glasgow)
DTSTART:20240123T143000Z
DTEND:20240123T153000Z
UID:TALK210541@talks.cam.ac.uk
CONTACT:Hanneke Wiersema
DESCRIPTION:The Breuil--Mézard conjecture concretely formulates the expec
 tation that\, under the Langlands correspondence\, natural congruences bet
 ween automorphic forms should be mirrored by congruences between Galois re
 presentations. In this talk I will explain some recent work which establis
 hes new cases of this conjecture for crystalline representations of a rami
 fied extension of Qp with small Hodge--Tate weights (roughly <= p/e). The 
 approach is purely local and revolves around a comparison between moduli s
 paces of such representations and more explicit closed subschemes inside t
 he affine grassmannian\, constructed as degenerations of products of flag 
 varieties. In particular\, the methods also apply to moduli of Galois repr
 esentations valued in more general split reductive groups than GLn.\n\n
LOCATION:MR13
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