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On higher order analogues of de Rham cohomology

Gabriele Vezzosi·Alexandre M. Vinogradov
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Abstract

If K is a commutative ring and A is a K-algebra, for any sequence $σ$ of positive integers there exists an higher order analogue dR($σ$) 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($σ$) does not depend on $σ$, 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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BibTeXRIS

Gabriele Vezzosi, Alexandre M. Vinogradov. 2000-02-19. On higher order analogues of de Rham cohomology. https://arxiv.org/abs/math/0002157

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