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Pop-up seminar in Number theory
Pop-up seminar in Number theory
Serre weight conjectures and modularity lifting for $\mathrm{GSp}_4$
Serre weight conjectures and modularity lifting for $\mathrm{GSp}_4$
组织者
演讲者
Heejong Lee
时间
2026年04月14日 14:00 至 15:00
地点
A3-3-201
线上
Zoom 559 700 6085
(BIMSA)
摘要
Given a Galois representation attached to a regular algebraic cuspidal automorphic representation, the Hodge-Tate weight of the Galois representation is matched with the weight of the automorphic representation. Serre weight conjectures are mod $p$ analogue of such a correspondence, relating ramification at $p$ of a mod $p$ Galois representation and Serre weights of mod $p$ algebraic automorphic forms. In this talk, I will discuss how to understand Serre weight conjectures and modularity lifting as a relationship between representation theory of finite groups of Lie type (e.g. $\mathrm{GSp}_4(\mathbb{F}_p)$) and the geometry of $p$-adic local Galois representations. Then I will explain the proof idea in the case of $\mathrm{GSp}_4$. This is based on a joint work with Daniel Le and Bao V. Le Hung.