CATEGORICAL PROPERTIES OF REDUCTION FUNCTORS OVER NON-POSITIVE DG-RINGS

Liran Shaul

doi:10.1090/proc/16517

CATEGORICAL PROPERTIES OF REDUCTION FUNCTORS OVER NON-POSITIVE DG-RINGS

Liran Shaul

Research output: Contribution to journal › Article › peer-review

Abstract

Given a non-positive DG-ring A, associated to it are the reduction and coreduction functors F(-) = H⁰(A)⊗^L_A- and G(-) = R Hom_A(H⁰(A), -), considered as functors D(A) → D(H⁰(A)), as well as the forgetful functor S : D(H⁰(A)) → D(A). In this paper we carry a systematic study of the categorical properties of these functors. As an application, a new descent result for vanishing of Ext and Tor over ordinary commutative noetherian rings is deduced.

Original language	English
Pages (from-to)	489-500
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	152
Issue number	2
DOIs	https://doi.org/10.1090/proc/16517
State	Published - 1 Feb 2024
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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title = "CATEGORICAL PROPERTIES OF REDUCTION FUNCTORS OVER NON-POSITIVE DG-RINGS",

abstract = "Given a non-positive DG-ring A, associated to it are the reduction and coreduction functors F(-) = H0(A)⊗LA- and G(-) = R HomA(H0(A), -), considered as functors D(A) → D(H0(A)), as well as the forgetful functor S : D(H0(A)) → D(A). In this paper we carry a systematic study of the categorical properties of these functors. As an application, a new descent result for vanishing of Ext and Tor over ordinary commutative noetherian rings is deduced.",

author = "Liran Shaul",

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N2 - Given a non-positive DG-ring A, associated to it are the reduction and coreduction functors F(-) = H0(A)⊗LA- and G(-) = R HomA(H0(A), -), considered as functors D(A) → D(H0(A)), as well as the forgetful functor S : D(H0(A)) → D(A). In this paper we carry a systematic study of the categorical properties of these functors. As an application, a new descent result for vanishing of Ext and Tor over ordinary commutative noetherian rings is deduced.

AB - Given a non-positive DG-ring A, associated to it are the reduction and coreduction functors F(-) = H0(A)⊗LA- and G(-) = R HomA(H0(A), -), considered as functors D(A) → D(H0(A)), as well as the forgetful functor S : D(H0(A)) → D(A). In this paper we carry a systematic study of the categorical properties of these functors. As an application, a new descent result for vanishing of Ext and Tor over ordinary commutative noetherian rings is deduced.

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ER -

CATEGORICAL PROPERTIES OF REDUCTION FUNCTORS OVER NON-POSITIVE DG-RINGS

Abstract

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