The plectic conjecture over local fields
Organizers
Hansheng Diao
, Yueke Hu
, Emmanuel Lecouturier
,
Cezar Lupu
Speaker
Siyan Daniel Li-Huerta
Time
Tuesday, September 27, 2022 10:00 AM - 11:00 AM
Venue
1118
Online
Zoom 293 812 9202
(BIMSA)
Abstract
The étale cohomology of varieties over Q enjoys a Galois action. For 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.