Number Theory Seminar | Martin Ortiz (University College London)

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

Abstract: The weight part of Serre's conjecture seeks to understand mod p congruences between automorphic forms of different weights. In the case of modular forms a key ingredient 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.

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