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arXiv · 0910.4724

Colocalization functors in derived categories and torsion theories

Shoham Shamir
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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.

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Shoham Shamir. 2010-08-28. Colocalization functors in derived categories and torsion theories. https://arxiv.org/abs/0910.4724

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