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arXiv · 1405.5299

Annihilation of cohomology and decompositions of derived categories

Srikanth B. Iyengar·Ryo Takahashi
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Abstract

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

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BibTeXRIS

Srikanth B. Iyengar, Ryo Takahashi. 2014-08-20. Annihilation of cohomology and decompositions of derived categories. https://arxiv.org/abs/1405.5299

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