Year: 2025
Type: preprint
Abstract: We essentially complete a program initiated by Boyarchenko--Weinstein to give a full description of the cohomology of deep level Deligne--Lusztig varieties for elliptic tori, with coefficients in arbitrary non-defining characteristics. We give several applications of our results: we show that the $ϕ$-weight part of the cohomology is very often concentrated in a single degree, and is induced from a Yu-type subgroup. Also, we give applications to a previous work of the second author on decomposition of deep level Deligne--Lusztig representations, and to Feng's explicit construction of Fargues--Scholze parameters. Furthermore, a conjecture of Chan--Oi about the Drinfeld stratification is verified as a special case from our results.
Source: arXiv (Cornell University)
Authors: Ivanov, Alexander B., Nie, Sian
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4416100792
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