Colocalization functors in derived categories and torsion theories

Abstract

Let R be a ring and let T be a hereditary torsion class of R-modules. The inclusion of the localizing subcategory generated by T into the derived category of R has a right adjoint, which is a colocalization. Benson has recently shown how to compute this right sdjoint when R is the group ring of a finite group over a prime field and T is the hereditary torsion class generated by a simple module. We generalize Benson's construction to the case where T is any hereditary torsion class on R. This yields an explicit formula for the colocalization with respect to T, using an injective cogenerator for T.

12 pages, detailed construction and extended examples