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Geometric weight conjecture for mod $p$ Hilbert modular forms

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Siqi Yang
Imperial College London
Fri, 15/09/2023 - 10:25 - 10:45
MPIM Lecture Hall
Serre’s Conjecture, proved by Khare and Wintenberger, shows that an odd, irreducible, mod $p$ representation of the absolute Galois group of $\mathbb{Q}$ comes from a mod $p$ modular eigenform. A generalisation to totally real fields has been conjectured by Buzzard, Jarvis and Diamond with the assumption that $p$ is unramified, where we have notions of algebraic weights and algebraic modularity. On the other hand, a representation is called geometrically modular if it comes from a mod $p$ Hilbert modular form. In this talk, I’ll discuss a link between geometric and algebraic modularities.


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