Modularity in the partial weight one case

Hanneke Wiersema (University of Cambridge)

Wednesday 16th November, 2022 16:00-17:00 Maths 311B

Abstract

Serre’s modularity conjecture, now a theorem of Khare and Wintenberger, asserts a connection between two-dimensional mod p Galois representations of the rationals and modular forms. The conjecture also predicts the minimal weight k≥2 such that a modular form of weight k corresponds to a given Galois representation. In this talk we discuss generalisations of this to more general Galois representations. In particular, we will study modularity in the case of partial weight one Hilbert modular forms, extending recent work of Diamond and Sasaki.

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