Filtrations and cohomology I: crystallization

Published 3 Nov 2025 in math.AG and math.AT | (2511.01567v1)

Abstract: We compare several different notions of filtered derived commutative ring, discussing HKR-filtered Hochschild homology, Hodge-filtered de Rham cohomology, and the lesser-known Hodge-filtered infinitesimal cohomology. Our main result is that de Rham cohomology is the crystallization of infinitesimal cohomology.

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Benjamin Antieau

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