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arXiv:1010.0351 [math.RT]AbstractReferencesReviewsResources

From triangulated categories to module categories via localisation

Aslak Bakke Buan, Robert J. Marsh

Published 2010-10-02, updated 2011-08-15Version 2

We show that the category of finite-dimensional modules over the endomorphism algebra of a rigid object in a Hom-finite triangulated category is equivalent to the Gabriel-Zisman localisation of the category with respect to a certain class of maps. This generalises the 2-Calabi-Yau tilting theorem of Keller-Reiten, in which the module category is obtained as a factor category, to the rigid case.

Comments: New section describing relationship to work of Nakaoka on cotorsion pairs. To appear in Transactions of the American Mathematical Society. 18 pages; no separate figures
Categories: math.RT, math.CT
Subjects: 16G20, 18E30, 18E35, 13F60
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