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Cohomological supports of tensor products of modules over commutative rings

Cohomological supports of tensor products of modules over commutative rings This works concerns cohomological support varieties of modules over commutative local rings. The main result is that the support of a derived tensor product of a pair of differential graded modules over a Koszul complex is the join of the supports of the modules. This generalizes, and gives another proof of, a result of Dao and the third author dealing with Tor-independent modules over complete intersection rings. The result for Koszul complexes has a broader applicability, including to exterior algebras over local rings. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

Cohomological supports of tensor products of modules over commutative rings

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG 2022
eISSN
2197-9847
DOI
10.1007/s40687-022-00321-7
Publisher site
See Article on Publisher Site

Abstract

This works concerns cohomological support varieties of modules over commutative local rings. The main result is that the support of a derived tensor product of a pair of differential graded modules over a Koszul complex is the join of the supports of the modules. This generalizes, and gives another proof of, a result of Dao and the third author dealing with Tor-independent modules over complete intersection rings. The result for Koszul complexes has a broader applicability, including to exterior algebras over local rings.

Journal

Research in the Mathematical Sciences – Springer Journals

Published: Jun 1, 2022

Keywords: Koszul complex; Dg modules; Cohomological support; Tensor products; Join; BGG correspondence; 13D02; 16E45 (primary); 13D07; 13H10 (secondary)

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