Homology, Homotopy and Applications

Volume 16 (2014)

Number 2

Annihilation of cohomology and decompositions of derived categories

Pages: 231 – 237

DOI: http://dx.doi.org/10.4310/HHA.2014.v16.n2.a12


Srikanth B. Iyengar (Department of Mathematics, University of Nebraska, Lincoln, Neb., U.S.A.)

Ryo Takahashi (Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, Japan)


It is proved that an element $r$ in the center of a coherent ring $\Lambda$ annihilates $\mathrm{Ext}^{n}_{\Lambda}(M,N)$, 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.


cohomology annihilator, derived category, projective class

2010 Mathematics Subject Classification

16E30, 16E35, 18G25

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Published 30 November 2014