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Nonnoetherian Grothendieck duality. (English) Zbl 0953.14013
Alonso Tarrío, Leovigildo et al., Studies in duality on noetherian formal schemes and non-noetherian ordinary schemes. Providence, RI: American Mathematical Society. Contemp. Math. 244, 115-123 (1999).
This paper is the third (and the last) of the series of papers of this volume. Let \(f:X\to Y\) be a separated morphism of quasi-compact, quasi-separated schemes. The author sketches a proof of the fact that the functor \({\mathbb R}f_*:{\mathbb D}^+_{qc}(X)\to{\mathbb D}^+(Y)\) has a right adjoint \(f^!\). Moreover, if \(f\) is proper, finitely presented and flat, then duality and tor-independent base-change hold for \(f^!\). The novelty of this paper is that the noetherian assumption of the schemes in question is dropped.
For the entire collection see [Zbl 0927.00024].

MSC:
14F99 (Co)homology theory in algebraic geometry
18A40 Adjoint functors (universal constructions, reflective subcategories, Kan extensions, etc.)
14A15 Schemes and morphisms
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