Hochschild (co)homology of the second kind I

Details Hochschild (co)homology of the second kind I Hochschild (co)homology of the second kind I

2010-10-05

arxiv.org/abs/1010.0982v2

Mathematics

Category Theory

LaTeX 2e, 67 pages. v.2: The case of matrix factorizations discussed in detail in the new subsections 4.8 and 4.10

Scientific paper

We define and study the Hochschild (co)homology of the second kind (known also as the Borel-Moore Hochschild homology and the compactly supported Hochschild cohomology) for curved DG-categories. An isomorphism between the Hochschild (co)homology of the second kind of a CDG-category B and the same of the DG-category C of right CDG-modules over B, projective and finitely generated as graded B-modules, is constructed. Sufficient conditions for an isomorphism of the two kinds of Hochschild (co)homology of a DG-category are formulated in terms of the two kinds of derived categories of DG-modules over it. In particular, a kind of "resolution of the diagonal" condition for the diagonal CDG-bimodule B over a CDG-category B guarantees an isomorphism of the two kinds of Hochschild (co)homology of the corresponding DG-category C. Several classes of examples are discussed.

Affiliated with

Also associated with

No associations

Rating

Hochschild (co)homology of the second kind I does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Hochschild (co)homology of the second kind I, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Hochschild (co)homology of the second kind I will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-87516