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Medientyp:
E-Artikel
Titel:
ANNIHILATORS AND DIMENSIONS OF THE SINGULARITY CATEGORY
Beteiligte:
LIU, JIAN
Erschienen:
Cambridge University Press (CUP), 2023
Erschienen in:Nagoya Mathematical Journal
Sprache:
Englisch
DOI:
10.1017/nmj.2022.45
ISSN:
0027-7630;
2152-6842
Entstehung:
Anmerkungen:
Beschreibung:
<jats:title>Abstract</jats:title><jats:p>Let <jats:italic>R</jats:italic> be a commutative Noetherian ring. We prove that if <jats:italic>R</jats:italic> is either an equidimensional finitely generated algebra over a perfect field, or an equidimensional equicharacteristic complete local ring with a perfect residue field, then the annihilator of the singularity category of <jats:italic>R</jats:italic> coincides with the Jacobian ideal of <jats:italic>R</jats:italic> up to radical. We establish a relationship between the annihilator of the singularity category of <jats:italic>R</jats:italic> and the cohomological annihilator of <jats:italic>R</jats:italic> under some mild assumptions. Finally, we give an upper bound for the dimension of the singularity category of an equicharacteristic excellent local ring with isolated singularity. This extends a result of Dao and Takahashi to non-Cohen–Macaulay rings.</jats:p>