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arXiv · 2208.09962

The plectic conjecture over local fields

Siyan Daniel Li-Huerta
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Abstract

Using a mixed-characteristic incarnation of fusion, we prove an analog of Nekov\'a\v{r}-Scholl's plectic conjecture for local Shimura varieties. We apply this to obtain results on the plectic conjecture for (global) Shimura varieties after restricting to a decomposition group. Along the way, we prove a $p$-adic uniformization theorem for the basic locus of abelian type Shimura varieties at hyperspecial level, which is of independent interest.

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Siyan Daniel Li-Huerta. 2022-08-21. The plectic conjecture over local fields. https://doi.org/10.1515/crelle-2025-0046

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