TL;DR
This paper presents two improved formulas for the top cohomology of tensor products of DG modules over nonpositive DG rings, simplifying calculations in derived algebraic contexts.
Contribution
It introduces two new, elementary formulas that extend the Kunneth trick to plain and derived tensor products over nonpositive DG rings.
Findings
New formula for top cohomology of plain tensor product
Extended Kunneth trick for derived tensor product
Elementary proofs provided
Abstract
The Kunneth trick is a formula for the top cohomology of the derived tensor product of two complexes of modules over a ring. In this note we present two improvements of this formula. The first improved Kunneth trick is a formula for the top cohomology of the plain tensor product of two DG modules over a nonpositive DG ring. The second trick handles the derived tensor product of two DG modules over a nonpositive DG ring. The proofs are elementary.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Commutative Algebra and Its Applications · Advanced Topics in Algebra