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SUMMARY:Theta linkage maps and the weight part of Serre's conjecture.  - M
 artin Ortiz (Imperial)
DTSTART:20241022T133000Z
DTEND:20241022T143000Z
UID:TALK220087@talks.cam.ac.uk
CONTACT:Jef Laga
DESCRIPTION: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 opera
 tor 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 appl
 ication I prove a generic entailment for the group GSp4\, i.e. a Hecke eig
 enform for a generic Serre weight in the lowest alcove is also modular for
  a Serre weight in one of the upper alcoves. 
LOCATION:MR13
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