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A duality theorem for the stable module category of representations of a finite group scheme is proved. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the $$\mathfrak{p}$$ -local and $$\mathfrak{p}$$ -torsion subcategories of the stable category, for each homogeneous prime ideal $$\mathfrak{p}$$ in the cohomology ring of the group scheme.
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LOCAL DUALITY FOR THE SINGULARITY CATEGORY OF A FINITE DIMENSIONAL GORENSTEIN ALGEBRA
A duality theorem for the singularity category of a finite dimensional Gorenstein algebra is proved. It complements a duality on the category of perfect complexes, discovered by Happel. One of its consequences is an analogue of Serre duality, and the existence of Auslander–Reiten triangles for the $$\mathfrak{p}$$ -local and $$\mathfrak{p}$$ -torsion subcategories of the derived category, for each homogeneous prime ideal $$\mathfrak{p}$$ arising from the action of a commutative ring via Hochschild cohomology.
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- PAR ID:
- 10180990
- Date Published:
- Journal Name:
- Nagoya Mathematical Journal
- ISSN:
- 0027-7630
- Page Range / eLocation ID:
- 1 to 24
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1017/nmj.2020.2
