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Homology of powers of regular ideals

Samuel Wüthrich
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Abstract

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 I^s and of R/I^s 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/I^s) and Tor_*^R(R/I, I^s) 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.

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Samuel Wüthrich. 2003-08-27. Homology of powers of regular ideals. https://arxiv.org/abs/math/0308263

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