On t-structures and Torsion Theories Induced by Compact Objects

Details On t-structures and Torsion Theories Induced by Compact Objects On t-structures and Torsion Theories Induced by Compact Objects

2000-05-17

arxiv.org/abs/math/0005172v1

Mathematics

Rings and Algebras

17 pages, AMSLaTeX

Scientific paper

First, we show that a compact object $C$ in a triangulated category, which satisfies suitable conditions, induces a $t$-structure. Second, in an abelian category we show that a complex $P^{\centerdot}$ of small projective objects of term length two, which satisfies suitable conditions, induces a torsion theory. In the case of module categories, using a torsion theory, we give equivalent conditions for $P^{\centerdot}$ to be a tilting complex. Finally, in the case of artin algebras, we give one to one correspondence between tilting complexes of term length two and torsion theories with certain conditions.

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