Dimensional vanishing of the saturated de Rham-Witt complex

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.