2010/12/17 by Peter Jørgensen, Peter Jorgensen, Jorgensen, Peter
Mathematics · #16E45 #18E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA) #math.RA #msc:16E45 #msc:18E30
paper · pdf · doi:10.48550/arxiv.1012.3888
18 pages
arxiv created 2010/12/17 · openalex publication_date 2010/12/17 · arxiv updated 2010/12/20 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
This paper develops a duality theory for connected cochain DG algebras, with particular emphasis on the non-commutative aspects. One of the main items is a dualizing DG module which induces a duality between the derived categories of DG left-modules and DG right-modules with finitely generated cohomology. As an application, it is proved that if the canonical module A / A≥ 1 has a semi-free resolution where the cohomological degree of the generators is bounded above, then the same is true for each DG module with finitely generated cohomology.