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SUMMARY:Multiplicity one and Breuil--Kisin cohomology of Shimura curves. -
  Andrea Dotto (University of Chicago)
DTSTART:20221129T143000Z
DTEND:20221129T153000Z
UID:TALK180425@talks.cam.ac.uk
CONTACT:Rong Zhou
DESCRIPTION:The multiplicity of Hecke eigenspaces in the mod p cohomology 
 of Shimura curves is a classical invariant which has been computed in sign
 ificant generality when the group splits at p. These results have recently
  found interesting applications to the mod p Langlands correspondence for 
 GL_2 over unramified p-adic fields. As a first step towards extending thes
 e to nonsplit quaternion algebras\, we prove a new multiplicity one theore
 m in the nonsplit case. The main idea of the proof is to use the Breuil--K
 isin module associated to a finite flat model of the cohomology to reduce 
 the problem to a known statement about modular forms on totally definite q
 uaternion algebras.
LOCATION:Zoom link: https://maths-cam-ac-uk.zoom.us/j/93515008077?pwd=NkZ5
 UGk2MTNueFhrb2c1RG96cFNPQT09
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