The Scholze-Shin conjecture in some cases

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• Alex Youcis
• Tuesday 29 October 2019, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Jack Thorne.

In 2013 Peter Scholze proved that the p-adic local Langlands conjecture for GL_n(F) can be explicitly characterized by a certain matching-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 | sigma(pi))=tr(f_tau | pi) where sigma(pi) is the image of pi under the local Langlands conjecture. In their 2013 paper Scholze and Sug Woo Shin conjectured a generalization of this result in the process of studying the cohomology of Shimura varieties for unitary similitude groups. In this talk we discuss ongoing work of the speaker and Alexander Bertoloni Meli on the solution to the Scholze-Shin conjecture for the unramified unitary groups and the relationship to the cohomology of unitary Shimura varieties.

This talk is part of the Number Theory Seminar series.

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