2000/02/19 by Gabriele Vezzosi, Vezzosi, Gabriele, A. M. Vinogradov +2
Mathematics · #13D25 #13N10 #58J10 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.AC #math.AG #math.RA #msc:13D25 #msc:13N10 #msc:58J10
paper · pdf · doi:10.48550/arxiv.math/0002157
Slightly revised version of Math. Preprint 19, Scuola Normale Superiore, Pisa (June 1998)
arxiv created 2000/02/19 · openalex publication_date 2000/02/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.