A case of the deformational Hodge conjecture via a pro Hochschild-Kostant-Rosenberg theorem

Abstract

Following ideas of Bloch, Esnault, and Kerz, the deformational part of Grothendieck's variational Hodge conjecture is established for proper, smooth schemes over $K[[t]]$, where $K$ is an algebraic extension of the rational numbers. The main tool is a pro Hochschild-Kostant-Rosenberg theorem for Hochschild homology.

French summary and publication information added

References in corpus (2)

• Relative continuous K-theory and cyclic homology
• Pro unitality and pro excision in algebraic K-theory and cyclic homology

Cited by in corpus (2)

• Pro unitality and pro excision in algebraic K-theory and cyclic homology
• Finite generation and continuity of topological Hochschild and cyclic homology