  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.
