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Number Theory Seminar

Title: Serre weights of certain mod $p$ Hilbert modular forms
Speaker: Abhik Ganguli (IISER Mohali)
Date: 24 November 2022
Time: 11.30 AM
Venue: LH-5

Let $F$ be a totally real field and $p$ be an odd prime unramified in $F$. We will give an overview of the problem of determining the explicit mod $p$ structure of a modular $p$-adic Galois representation and determining the associated local Serre weights. The Galois representations are attached to Hilbert modular forms over $F$, more precisely to eigenforms on a Shimura curve over $F$. The weight part of the Serre’s modularity conjecture for Hilbert modular forms relates the local Serre weights at a place $v|p$ to the structure of the mod $p$ Galois representation at the inertia group over $v$. Thus, local Serre weights give good information on the structure of the modular mod $p$ Galois representation. The eigenforms considered are of small slope at a fixed place $\mathbf{p}|p$, and with certain constraints on the weight over $\mathbf{p}$. This is based on a joint work with Shalini Bhattacharya.

Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 08 Dec 2022