Cohomological supports over derived complete intersections and local rings
Abstract
A theory of cohomological support for pairs of DG modules over a Koszul complex is investigated. These specialize to the support varieties of Avramov and Buchweitz defined over a complete intersection ring, as well as support varieties over an exterior algebra. The main objects of study are certain DG modules over a polynomial ring; these determine the aforementioned cohomological supports and are shown to encode (co)homological information about pairs of DG modules over a Koszul complex. The perspective in this article leads to new proofs of well-known results for pairs of complexes over a complete intersection. Furthermore, these cohomological supports are used to define a support theory for pairs of objects in the derived category of an arbitrary commutative noetherian local ring. Finally, we calculate several examples and provide an application by answering a question of D. Jorgensen in the negative.
Cite
@article{arxiv.1912.12009,
title = {Cohomological supports over derived complete intersections and local rings},
author = {Josh Pollitz},
journal= {arXiv preprint arXiv:1912.12009},
year = {2021}
}
Comments
40 pages. V2: New introduction and minor changes. To appear in Math. Zeit