Theta linkage maps and the weight part of Serre's conjecture.

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• Martin Ortiz (Imperial)
• Tuesday 22 October 2024, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jef Laga.

The weight part of Serre’s conjecture seeks to understand mod p congruences between automorphic forms of different weights. For modular forms a key ingredient in its proof was Edixhoven’s use of the theta operator on the modular curve. I will explain the construction of a new family of theta operators on Shimura varieties, and how they are related to the conjectures of Herzig on the weight part of Serre’s conjecture. As an application I prove a generic entailment for the group GSp4, i.e. a Hecke eigenform for a generic Serre weight in the lowest alcove is also modular for a Serre weight in one of the upper alcoves.

This talk is part of the Number Theory Seminar series.

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