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Recollement of homotopy categories and Cohen-Macaulay modules

Published online by Cambridge University Press:  04 November 2011

Osamu Iyama ,
Kiriko Kato  and
Jun-ichi Miyachi
Osamu Iyama
Affiliation:
Graduate School of Mathematics, Nagoya University Chikusa-ku, Nagoya, 464-8602Japaniyama@math.nagoya-u.ac.jp
Kiriko Kato
Affiliation:
Graduate School of Science, Osaka Prefecture University, 1-1 Gakuen-cho, Nakaku, Sakai, Osaka 599-8531, Japankiriko@mi.s.osakafu-u.ac.jp
Jun-ichi Miyachi
Affiliation:
Department of Mathematics, Tokyo Gakugei University, Koganei-shi, Tokyo, 184-8501Japanmiyachi@u-gakugei.ac.jp
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Abstract

We study the homotopy category of unbounded complexes with bounded homologies and its quotient category by the homotopy category of bounded complexes. In the case of the homotopy category of finitely generated projective modules over an Iwanaga-Gorenstein ring, we show the existence of a new structure in the above quotient category, which we call a triangle of recollements. Moreover, we show that this quotient category is triangle equivalent to the stable module category of Cohen-Macaulay T2(R)-modules.

Keywords

triangulated categorytriangle of recollementshomotopy categoryIwanaga-Gorenstein ringCohen-Macaulay module

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Type
Research Article
Information
Journal of K-Theory , Volume 8 , Issue 3 , December 2011 , pp. 507 - 542
Copyright
Copyright © ISOPP 2011

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