Derived category of Finite Spaces and Grothendieck Duality

Fernando Sancho de Salas; Juan Francisco Torres Sancho

Derived category of Finite Spaces and Grothendieck Duality

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arxiv 1904.06935 v1 pith:P3PR4SBE submitted 2019-04-15 math.AG

Fernando Sancho de Salas , Juan Francisco Torres Sancho This is my paper · ORCID

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keywords categoryderiveddualityfinitegrothendieckresultsringedspaces

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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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Grothendieck Duality theories -- abstract and concrete, I: pseudo-coherent finite maps
math.AG 2019-08 conditional novelty 6.0 of 10

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.

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