✦ LIBER ✦

On t-structures and torsion theories induced by compact objects

✍ Scribed by Mitsuo Hoshino; Yoshiaki Kato; Jun-Ichi Miyachi

Book ID: 104152408
Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 175 KB
Volume: 167
Category: Article
ISSN: 0022-4049
DOI: 10.1016/s0022-4049(01)00012-3

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✦ Synopsis

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

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