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

L. L. Avramov, R. -O. Buchweitz, L. M. Sega

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 con…