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- Title
Relation between two twisted inverse image pseudofunctors in duality theory.
- Authors
Iyengar, Srikanth B.; Lipman, Joseph; Neeman, Amnon
- Abstract
Grothendieck duality theory assigns to essentially finite-type maps $f$ of noetherian schemes a pseudofunctor $f^{\times }$ right-adjoint to $\mathsf{R}f_{\ast }$, and a pseudofunctor $f^{!}$ agreeing with $f^{\times }$ when $f$ is proper, but equal to the usual inverse image $f^{\ast }$ when $f$ is étale. We define and study a canonical map from the first pseudofunctor to the second. This map behaves well with respect to flat base change, and is taken to an isomorphism by ‘compactly supported’ versions of standard derived functors. Concrete realizations are described, for instance for maps of affine schemes. Applications include proofs of reduction theorems for Hochschild homology and cohomology, and of a remarkable formula for the fundamental class of a flat map of affine schemes.
- Subjects
INVERSE functions; DUALITY theory (Mathematics); IMAGE processing; MATHEMATICAL mappings; NOETHERIAN rings; ISOMORPHISM (Mathematics)
- Publication
Compositio Mathematica, 2015, Vol 151, Issue 4, p735
- ISSN
0010-437X
- Publication type
Article
- DOI
10.1112/S0010437X14007672