An Auslander-Reiten principle in derived categories

Maiko Ono; Yuji Yoshino

An Auslander-Reiten principle in derived categories

Maiko Ono, Yuji Yoshino

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Abstract

We give a principle in derived categories, which lies behind the classical Auslander-Reiten duality and its generalized version by Iyama and Wemyss. We apply the principle to show the validity of the Auslander-Reiten conjecture over a Gorenstein ring in the case where the ring has dimension larger than two and the singular locus has at most one dimension.

Original language	Undefined/Unknown
Journal	Journal of Pure and Applied Algebra
Publication status	Published - May 15 2018

Keywords

math.AC
13D09, 13C14, 16G50

Access to Document

1805.05676v1

Cite this

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title = "An Auslander-Reiten principle in derived categories",

abstract = " We give a principle in derived categories, which lies behind the classical Auslander-Reiten duality and its generalized version by Iyama and Wemyss. We apply the principle to show the validity of the Auslander-Reiten conjecture over a Gorenstein ring in the case where the ring has dimension larger than two and the singular locus has at most one dimension. ",

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journal = "Journal of Pure and Applied Algebra",

issn = "0022-4049",

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AU - Yoshino, Yuji

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Y1 - 2018/5/15

N2 - We give a principle in derived categories, which lies behind the classical Auslander-Reiten duality and its generalized version by Iyama and Wemyss. We apply the principle to show the validity of the Auslander-Reiten conjecture over a Gorenstein ring in the case where the ring has dimension larger than two and the singular locus has at most one dimension.

AB - We give a principle in derived categories, which lies behind the classical Auslander-Reiten duality and its generalized version by Iyama and Wemyss. We apply the principle to show the validity of the Auslander-Reiten conjecture over a Gorenstein ring in the case where the ring has dimension larger than two and the singular locus has at most one dimension.

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KW - 13D09, 13C14, 16G50

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JO - Journal of Pure and Applied Algebra

JF - Journal of Pure and Applied Algebra

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