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Convex elements and cohomology of deep level Deligne-Lusztig varieties

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arxiv 2503.13412 v2 pith:DSK6SAFB submitted 2025-03-17 math.AG math.RT

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keywords cohomologydeepgivelevelapplicationsdeligne--lusztigresultsvarieties
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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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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Green functions for positive-depth Deligne--Lusztig induction

    math.RT 2025-06 accept novelty 7.0 of 10

    For large q, positive-depth Deligne-Lusztig induction matches the Yu-Kaletha-FKS algebraic construction for all Howe-unramified elliptic pairs, via a characterization theorem and a Green function comparison.

  2. An explicit decomposition of higher Deligne-Lsuztig representations

    math.RT 2025-06 conditional novelty 6.0 of 10

    For q ≥ c_Λ with 2 ≤ c_Λ ≤ 4, the geometric representation κ_Λ from cohomology of higher Deligne-Lusztig varieties equals κ(Λ)⊗ϵ_Λ, giving an explicit irreducible decomposition of elliptic higher Deligne-Lusztig repre...

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