On higher order analogues of de Rham cohomology

Details On higher order analogues of de Rham cohomology On higher order analogues of de Rham cohomology

2000-02-19

arxiv.org/abs/math/0002157v1

Mathematics

Rings and Algebras

Slightly revised version of Math. Preprint 19, Scuola Normale Superiore, Pisa (June 1998)

Scientific paper

If K is a commutative ring and A is a K-algebra, for any sequence $\sigma $ of positive integers there exists an higher order analogue dR($\sigma $) of the standard de Rham complex dR(1,...,1,...), which can also be defined starting from suitable ("differentially closed") subcategories of (A-mod). The main result of this paper is that the cohomology of dR($\sigma $) does not depend on $\sigma $, under some smoothness assumptions on the ambient category. Before proving the main theorem we give a rather detailed exposition of all relevant (to our present purposes) functors of differential calculus on commutative algebras. This part can be also of an independent interest.

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