Decomposition of de Rham complex for quasi-F-split varieties
Algebraic Geometry
2025-02-20 v1
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.
Keywords
Cite
@article{arxiv.2502.13356,
title = {Decomposition of de Rham complex for quasi-F-split varieties},
author = {Alexander Petrov},
journal= {arXiv preprint arXiv:2502.13356},
year = {2025}
}
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