2004/06/03 by Oana Veliche, Veliche, Oana · 1 citation
Mathematics · #18Gxx #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Rings and Algebras (math.RA) #math.AC #math.RA #msc:18Gxx
paper · pdf · doi:10.48550/arxiv.math/0406057
Accepted for publication in Transactions AMS, submitted October 8, 2003
arxiv created 2004/06/03 · openalex publication_date 2004/06/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define and study a notion of Gorenstein projective dimension for complexes of left modules over associative rings. For complexes of finite Gorenstein projective dimension we define and study a Tate cohomology theory. Tate cohomology groups have a natural transformation to classical Ext groups. In the case of module arguments, we show that these maps fit into a long exact sequence, where every third term is a relative cohomology group defined for left modules of finite Gorenstein projective dimension.