Exponentially twisted cyclic homology

TL;DR

This paper extends the isomorphism between de Rham cohomology and periodic cyclic homology to twisted settings involving exponential functions, with implications for derived invariance of algebraic Gauss-Manin systems.

Contribution

It demonstrates that Keller's isomorphism persists in the twisted case and explores consequences for derived invariance of Gauss-Manin systems.

Findings

Isomorphism holds in twisted setting

Derived invariance of algebraic Gauss-Manin systems

Extension of Keller's theorem to exponential twists

Abstract

By a theorem of Bernhard Keller the de Rham cohomology of a smooth variety is isomorphic to the periodic cyclic homology of the differential graded category of perfect complexes on the variety. Both the de Rham cohomology and the cyclic homology can be twisted by the exponential of a regular function on the variety. We explain that the isomorphism holds true in the twisted setting and draw some conclusions on derived invariance of the algebraic Gauss-Manin systems associated with regular functions.