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An improvement on the base-change theorem and the functor $f^!$

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arxiv 1406.7599 v3 pith:7CBFC42W submitted 2014-06-30 math.AG

Amnon Neeman This is my paper · ORCID
classification math.AG
keywords dualityfunctorgrothendieckimprovementalgebraicavramovbase-changecame
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abstract

The major improvement in this paper is that we can extend the functor $(-)^!$ of Grothendieck duality to the unbounded derived category of sufficiently nice algebraic stacks. The original motivation came from formulas discovered by Avramov and Iyengar, linking Grothendieck duality with Hochscild homology and cohomology.

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  1. 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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