Grothendieck duality for non-proper morphisms

2018/10/14 by Tobias Schedlmeier, Schedlmeier, Tobias
Mathematics · #14B15 (Secondary) #14N30 (Primary) #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1810.06082

openalex publication_date 2018/10/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We generalize the adjunction between the functors Rf_* and f^! of derived categories of quasi-coherent sheaves for proper morphisms f\colon X → Y of Noetherian schemes to the following situation: Let f be a finite type morphism and let Z' ⊆ X and Z ⊆ Y be closed subsets such that f restricts to a proper morphism f'\colon Z'→ Z of f. Then the functor Rf_* is left adjoint to RΓ_Z'f^! when considered as functors between complexes supported on Z' or Z.

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