Colocalization functors in derived categories and torsion theories

Shoham Shamir

Let R be a ring and let A be a hereditary torsion class of R-modules. The inclusion of the localizing subcategory generated by A into the derived category of R has a right adjoint, denoted Cell_A. Recently, Benson has shown how to compute Cell_A R when R is a group ring of a finite group over a prime field and A is the hereditary torsion class generated by a simple module. We generalize Benson's construction to the case where A is any hereditary torsion class on R. It is shown that for every R-module M there exists an injective R-module E such that:

Hn(CellA M) ≅ ExtEndR(E)n-1(HomR(M,E),E) for n ≥ 2.

Homology, Homotopy and Applications, Vol. 13 (2011), No. 1, pp.75-88.

doi:10.4310/HHA.2011.v13.n1.a3

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