Local duality for the singularity category of a finite dimensional Gorenstein algebra
| Autor: | Dave Benson, Henning Krause, Julia Pevtsova, Srikanth B. Iyengar |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
General Mathematics
Prime ideal Duality (mathematics) Serre duality Commutative ring 16G10 (primary) 16G50 16E65 16E35 01 natural sciences Singularity Mathematics::K-Theory and Homology Mathematics::Category Theory 0103 physical sciences FOS: Mathematics Representation Theory (math.RT) 0101 mathematics Mathematics::Representation Theory Mathematics Derived category Mathematics::Commutative Algebra 010102 general mathematics Mathematics::Rings and Algebras 16. Peace & justice Cohomology Algebra Torsion (algebra) 010307 mathematical physics Mathematics - Representation Theory |
| Popis: | 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. 19 pages |
| Databáze: | OpenAIRE |
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