Dimensional vanishing of the saturated de Rham-Witt complex
Algebraic Geometry
2025-12-15 v2
Abstract
The saturated de Rham-Witt complex, introduced by Bhatt-Lurie-Mathew in arXiv:1805.05501, is a variant of the classical de Rham-Witt complex which is expected to behave better for singular schemes. We provide partial justification for this expectation by showing that the saturated de Rham-Witt complex satisfies a dimensional vanishing property even in the presence of singularities. This is stronger than the vanishing properties of the classical de Rham-Witt complex, crystalline cohomology, or de Rham cohomology, and is instead comparable to \'etale cohomology.
Keywords
Cite
@article{arxiv.2507.22314,
title = {Dimensional vanishing of the saturated de Rham-Witt complex},
author = {Ravi Fernando},
journal= {arXiv preprint arXiv:2507.22314},
year = {2025}
}
Comments
9 pages; minor fix to Lemma 2.1, added a brief remark on future directions