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Quotient triangulated categories

Xiao-Wu Chen·Pu Zhang
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Abstract

For a self-orthogonal module $T$, the relation between the quotient triangulated category $D^b(A)/K^b({\rm add} T)$ and the stable category of the Frobenius category of $T$-Cohen-Macaulay modules is investigated. In particular, for a Gorenstein algebra, we get a relative version of the description of the singularity category due to Happel. Also, the derived category of a Gorenstein algebra is explicitly given, inside the stable category of the graded module category of the corresponding trivial extension algebra, via Happel's functor $F: D^b(A) \longrightarrow T(A)^{\mathbb{Z}}{-}\underline{\rm mod}$.

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Xiao-Wu Chen, Pu Zhang. 2007-03-31. Quotient triangulated categories. https://arxiv.org/abs/math/0601489

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