Coherent rings, fp-injective modules, dualizing complexes, and covariant Serre–Grothendieck duality
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Leonid Positselski [1]
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[1] Higher School of Economics, National Research University
Higher School of Economics, National Research University
Rusia
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- Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 2, 2017, págs. 1279-1307
- Idioma: inglés
- Enlaces
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Resumen
For a left coherent ring A with every left ideal having a countable set of generators, we show that the coderived category of left A-modules is compactly generated by the bounded derived category of finitely presented left A-modules (reproducing a particular case of a recent result of Št’ovíˇcek with our methods). Furthermore, we present the definition of a dualizing complex of fp-injective modules over a pair of noncommutative coherent rings A and B, and construct an equivalence between the coderived category of A-modules and the contraderived category of B-modules.
Finally, we define the notion of a relative dualizing complex of bimodules for a pair of noncommutative ring homomorphisms A −→ R and B −→ S, and obtain an equivalence between the R/A-semicoderived category of R-modules and the S/Bsemicontraderived category of S-modules. For a homomorphism of commutative rings A −→ R, we also construct a tensor structure on the R/A-semicoderived category of R-modules. A vision of semi-infinite algebraic geometry is discussed in the introduction.
