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arXiv · 2503.13412

Convex elements and cohomology of deep level Deligne-Lusztig varieties

Alexander B. Ivanov·Sian Nie
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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 $\phi$-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.

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Alexander B. Ivanov, Sian Nie. 2025-03-17. Convex elements and cohomology of deep level Deligne-Lusztig varieties. https://arxiv.org/abs/2503.13412

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