For pseudo-coherent finite maps of schemes, this preprint proves the concrete dualizing pseudofunctor f^♭ is isomorphic to the abstract f^!, and gives explicit comparisons for tensor, Hom, and Koszul-regular immersions.
Derived category of Finite Spaces and Grothendieck Duality
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abstract
We obtain some fundamental results, as Bokstedt-Neeman Theorem and Grothendieck duality, about the derived category of modules on a finite ringed space. Then we see how these results are transfered to schemes in a simple way and generalized to other ringed spaces.
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2019 1verdicts
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Grothendieck Duality theories -- abstract and concrete, I: pseudo-coherent finite maps
For pseudo-coherent finite maps of schemes, this preprint proves the concrete dualizing pseudofunctor f^♭ is isomorphic to the abstract f^!, and gives explicit comparisons for tensor, Hom, and Koszul-regular immersions.