Automorphy Lifting with Ĝ-adequate image

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• Dmitri Whitmore (Cambridge)
• Tuesday 24 January 2023, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Rong Zhou.

Let F be a number field and G a reductive group. The Langlands program attempts to relate

(1) automorphic representations of G

(2) representations of the absolute Galois group of F valued in Ĝ, the dual group of G.

Automorphy lifting theorems are a way to go from (2) to (1). Such theorems are proved using the Taylor—Wiles method but require certain ‘big image’ hypotheses.

We discuss a generalization and the resulting weakened big image condition (Ĝ-adequate image). We also explore aspects of the Galois deformation theory used in our variant. We conclude with applications to modularity of some elliptic curves over quadratic extensions of totally real fields, building on work of Boxer—Calegari—Gee—Pilloni.

This talk is part of the Number Theory Seminar series.

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