### The weight part of Serre's modularity conjecture for totally real fields

Linfoot Number Theory Seminar

24th November 2021, 11:00 am – 12:00 pm

Fry Building, Room 2.04

The strong form of Serre's modularity conjecture states that every two-dimensional continuous, odd, irreducible mod p representation of the absolute Galois group of Q arises from a modular form of a specific minimal weight, level and character. We show this minimal weight is equal to two other notions of minimal weight, one inspired by work of Buzzard, Diamond and Jarvis and one coming from p-adic Hodge theory. We discuss the interplay between these three characterisations of the weight for Galois representations over totally real fields and investigate the consequences for generalised Serre conjectures.

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