Modularity of certain trianguline Galois representations

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• James Kiln (Queen Mary)
• Tuesday 27 May 2025, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jef Laga.

An unpublished result of Emerton states that every trianguline representation of the absolute Galois group of Q, satisfying certain conditions, arises as a twist of the Galois representation attached to an overconvergent p-adic cuspidal eigenform of finite slope. I will outline a new approach to prove this result by patching trianguline varieties and eigenvarieties for modular forms on GL2 to establish an “R=T” theorem in the setting of rigid analytic spaces. There are several nice consequences to such a theorem, including a new approach to deduce the classicality of overconvergent eigenforms of small slope, as well as applications to the Fontaine-Mazur conjecture.

This talk is part of the Number Theory Seminar series.

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