On higher order analogues of de Rham cohomology
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- February 2000
- DOI:
- 10.48550/arXiv.math/0002157
- arXiv:
- arXiv:math/0002157
- Bibcode:
- 2000math......2157V
- Keywords:
-
- Mathematics - Rings and Algebras;
- Mathematics - Commutative Algebra;
- Mathematics - Algebraic Geometry;
- 13N10;
- 13D25;
- 58J10
- E-Print:
- Slightly revised version of Math. Preprint 19, Scuola Normale Superiore, Pisa (June 1998)