2020/06/15 by Yang Xiaoyan, Yang, Xiaoyan
Mathematics · #13D45 #18E30 #18E35 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2006.08065
openalex publication_date 2020/06/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The goal of the article is to better understand cosupport in triangulated categories since it is still quite mysterious. We study boundedness of local cohomology and local homology functors using Koszul objects, give some characterizations of cosupport and get some results that, in special cases, recover and generalize the known results about the usual cosupport. Also we include some computations of cosupport, settle the comparison of support and cosupport of cohomologically finite objects. Finally, we assign to any object of the category a subset of SpecR, called the big cosupport.