Multiplicity one and Breuil--Kisin cohomology of Shimura curves.

Add to your list(s) Download to your calendar using vCal

• Andrea Dotto (University of Chicago)
• Tuesday 29 November 2022, 14:30-15:30
• Zoom link: https://maths-cam-ac-uk.zoom.us/j/93515008077?pwd=NkZ5UGk2MTNueFhrb2c1RG96cFNPQT09.

If you have a question about this talk, please contact Rong Zhou.

The multiplicity of Hecke eigenspaces in the mod p cohomology of Shimura curves is a classical invariant which has been computed in significant 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 these to nonsplit quaternion algebras, we prove a new multiplicity one theorem in the nonsplit case. The main idea of the proof is to use the Breuil—Kisin module associated to a finite flat model of the cohomology to reduce the problem to a known statement about modular forms on totally definite quaternion algebras.

This talk is part of the Number Theory Seminar series.

This talk is included in these lists:

• All CMS events
• All Talks (aka the CURE list)
• CMS Events
• DPMMS Lists
• DPMMS Pure Maths Seminar
• DPMMS info aggregator
• DPMMS lists
• Hanchen DaDaDash
• Interested Talks
• Number Theory Seminar
• School of Physical Sciences
• Zoom link: https://maths-cam-ac-uk.zoom.us/j/93515008077?pwd=NkZ5UGk2MTNueFhrb2c1RG96cFNPQT09
• bld31

Note that ex-directory lists are not shown.