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arXiv · 0911.0172

Recollement of homotopy categories and Cohen-Macaulay modules

Osamu Iyama·Kiriko Kato·Jun-ichi Miyachi
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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. We show the existence of a recollement of the above quotient category and it has the homotopy category of acyclic complxes as a triangulated subcategory. In the case of the homotopy category of finitely generated projective modules over an Iwanaga-Gorenstein ring, we show that the above quotient category are triangle equivalent to the stable module category of Cohen-Macaulay $\opn{T}_2(R)$-modules.

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Osamu Iyama, Kiriko Kato, Jun-ichi Miyachi. 2010-01-06. Recollement of homotopy categories and Cohen-Macaulay modules. https://arxiv.org/abs/0911.0172

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