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SUMMARY:Automorphy Lifting with Ĝ-adequate image - Dmitri Whitmore (Cambr
 idge)
DTSTART:20230124T143000Z
DTEND:20230124T153000Z
UID:TALK195355@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:Let F be a number field and G a reductive group. The Langlands
  program attempts to relate\n\n(1) automorphic representations of G\n\n(2)
  representations of the absolute Galois group of F valued in Ĝ\, the dual
  group of G.\n\nAutomorphy lifting theorems are a way to go from (2) to (1
 ). Such theorems are proved using the Taylor--Wiles method but require cer
 tain 'big image' hypotheses.\n\nWe discuss a generalization and the result
 ing weakened big image condition (Ĝ-adequate image). We also explore aspe
 cts of the Galois deformation theory used in our variant. We conclude with
  applications to modularity of some elliptic curves over quadratic extensi
 ons of totally real fields\, building on work of Boxer--Calegari--Gee--Pil
 loni.
LOCATION:MR13
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