On higher order analogues of de Rham cohomology
| Autor: | Gabriele Vezzosi, A. M. Vinogradov |
|---|---|
| Rok vydání: | 2003 |
| Předmět: |
Pure mathematics
13D25 13N10 58J10 Commutative ring Commutative Algebra (math.AC) Differentially closed field Mathematics - Algebraic Geometry Jets FOS: Mathematics De Rham cohomology Algebraic Geometry (math.AG) Algebraic differential forms Differential operators Commutative property Mathematics Chern–Weil homomorphism Differential calculus Mathematics - Rings and Algebras Mathematics - Commutative Algebra Differential operator Algebra Closed and exact differential forms Computational Theory and Mathematics Rings and Algebras (math.RA) Geometry and Topology Analysis |
| Zdroj: | Differential Geometry and its Applications. 19(1):29-59 |
| ISSN: | 0926-2245 |
| DOI: | 10.1016/s0926-2245(03)00014-7 |
| Popis: | 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. Comment: Slightly revised version of Math. Preprint 19, Scuola Normale Superiore, Pisa (June 1998) |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect