The telescope conjecture for hereditary rings via Ext-orthogonal pairs

Details The telescope conjecture for hereditary rings via Ext-orthogonal pairs The telescope conjecture for hereditary rings via Ext-orthogonal pairs

2008-10-08

arxiv.org/abs/0810.1401v5

Adv. Math. 225 (2010) 2341-2364

Mathematics

Representation Theory

22 pages, minor changes, final version, to appear in "Advances in Mathematics".

Scientific paper

10.1016/j.aim.2010.04.027

For the module category of a hereditary ring, the Ext-orthogonal pairs of subcategories are studied. For each Ext-orthogonal pair that is generated by a single module, a 5-term exact sequence is constructed. The pairs of finite type are characterized and two consequences for the class of hereditary rings are established: homological epimorphisms and universal localizations coincide, and the telescope conjecture for the derived category holds true. However, we present examples showing that neither of these two statements is true in general for rings of global dimension 2.

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