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SUMMARY:The Scholze-Shin conjecture in some cases - Alex Youcis
DTSTART:20191029T143000Z
DTEND:20191029T153000Z
UID:TALK130033@talks.cam.ac.uk
CONTACT:Jack Thorne
DESCRIPTION:In 2013 Peter Scholze proved that the p-adic local Langlands c
 onjecture for GL_n(F) can be explicitly characterized by a certain matchin
 g-trace-condition. Very roughly it says that for every tau in W_F there is
  a function f_tau in the Hecke algebra for GL_n(F) such that tr(tau | sigm
 a(pi))=tr(f_tau | pi) where sigma(pi) is the image of pi under the local L
 anglands conjecture. In their 2013 paper Scholze and Sug Woo Shin conjectu
 red a generalization of this result in the process of studying the cohomol
 ogy of Shimura varieties for unitary similitude groups. In this talk we di
 scuss ongoing work of the speaker and Alexander Bertoloni Meli on the solu
 tion to the Scholze-Shin conjecture for the unramified unitary groups and 
 the relationship to the cohomology of unitary Shimura varieties. 
LOCATION:MR13
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