arXiv Open Access 2002

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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Abstrak

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.

Topik & Kata Kunci

math.AC

Penulis (3)

L. L. Avramov

R. -O. Buchweitz

L. M. Sega

Format Sitasi

APA MLA BibTeX

Avramov, L.L., Buchweitz, R.-., Sega, L.M. (2002). Extensions of a Dualizing Complex by its Ring: Commutative Versions of a Conjecture of Tachikawa. https://arxiv.org/abs/math/0208172

Akses Cepat

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Informasi Jurnal

Tahun Terbit: 2002
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓