Number Theory

Title: The plectic conjecture over local fields
Speaker: Daniel Li
Speaker Info: Harvard University
Brief Description:
Special Note:

The étale cohomology of varieties over Q enjoys a Galois action. In the case of Hilbert modular varieties, Nekovář-Scholl observed that this Galois action on the level of cohomology extends to a much larger profinite group: the plectic group. Motivated by applications to higher-rank Euler systems, they conjectured that this extension holds even on the level of complexes, as well as for more general Shimura varieties.

We present a proof of the analog of this conjecture for local Shimura varieties. Consequently, we obtain results for the basic locus of global Shimura varieties, after restricting to a decomposition group. The proof crucially uses a mixed-characteristic version of fusion due to Fargues-Scholze.

Date: Friday, October 28, 2022
Time: 2:00PM
Where: Tech L160
Contact Person: Bao Le Hung
Contact email: lhvietbao@math.northwestern.edu
Contact Phone:
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