Quotient triangulated categories

Abstract

For a self-orthogonal module $T$, the relation between the quotient triangulated category $D^b(A)/K^b(\mathrm{add}T)$ 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 $F:D^b(A)⟶T(A{)}^{\mathbb{Z}}-\underline{\mathrm{mod}}$.

14 pages. Manu. Math., to appear