Decomposition of de Rham complex for quasi-F-split varieties

2025/02/19 by Alexander Petrov, Petrov, Alexander · 2 citations
Computer Science · Mathematics · #14F40 #14G17 (Primary) 20G40 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2502.13356

openalex publication_date 2025/02/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the de Rham stack of Bhatt-Lurie and Drinfeld, we prove that de Rham complex of a smooth quasi-F-split variety over a perfect field of positive characteristic decomposes in all degrees. In particular, smooth proper quasi-F-split varieties have degenerate Hodge-to-de Rham spectral sequence, and satisfy Kodaira-Akizuki-Nakano vanishing. We apply this to prove that the Hodge-to-de Rham spectral sequence for the classifying stack of a reductive group over a field of positive characteristic degenerates.

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