2003/08/27 by Samuel Wüthrich, Wüthrich, Samuel
Mathematics · #13D02 #13D07 (Primary) #55U15 (Secondary) #Algebraic Topology (math.AT) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AT #msc:13D02 #msc:13D07 #msc:55U15
paper · pdf · doi:10.48550/arxiv.math/0308263
11 pages
arxiv created 2003/08/27 · arxiv updated 2009/12/01
For a commutative ring R with an ideal I, generated by a finite regular sequence, we construct differential graded algebras which provide R-free resolutions of Is and of R/Is for s>0 and which generalise the Koszul resolution. We derive these from a certain multiplicative double complex. By means of a Cartan-Eilenberg spectral sequence we express Tor_*R(R/I,R/Is) and Tor_*R(R/I, Is) in terms of exact sequences and find that they are free as R/I-modules. Except for R/I, their product structure turns out to be trivial; instead, we consider an exterior product. The paper is based on ideas by Andrew Baker; it is written in view of applications to algebraic topology.