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Extensions of a Dualizing Complex by its Ring: Commutative Versions of a Conjecture of Tachikawa

L. L. Avramov·R. -O. Buchweitz·L. M. Sega
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Abstract

Let $(R,\fm,k)$ be a commutative noetherian local ring with dualizing complex $\dua R$, normalized by $\Ext^{\depth(R)}_R(k,\dua R)\cong k$. Partly motivated by a long standing conjecture of Tachikawa on (not necessarily commutative) $k$-algebras of finite rank, we conjecture that if $\Ext^n_R(\dua R,R)=0$ for all $n>0$, then $R$ is Gorenstein, and prove this in several significant cases.

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L. L. Avramov, R. -O. Buchweitz, L. M. Sega. 2003-03-16. Extensions of a Dualizing Complex by its Ring: Commutative Versions of a Conjecture of Tachikawa. https://arxiv.org/abs/math/0208172

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