Annihilation of cohomology and decompositions of derived categories

Abstract

It is proved that an element $r$ in the center of a coherent ring $\Lambda$ annihilates ${\mathrm{Ext}}_{\Lambda }^n(M,N)$, for some positive integer $n$ and all finitely presented $\Lambda$-modules $M$ and $N$, if and only if the bounded derived category of $\Lambda$ is an extension of the subcategory consisting of complexes annihilated by $r$ and those obtained as $n$-fold extensions of $\Lambda$. This has applications to finiteness of dimension of derived categories.

6 pages. To appear in Homology, Homotopy and Applications

References in corpus (1)

• Annihilation of cohomology and strong generation of module categories