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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.