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Award ID contains: 1201889

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  1. ; ; (, Mathematical Proceedings of the Cambridge Philosophical Society)
    Abstract Local cohomology functors are constructed for the category of cohomological functors on an essentially small triangulated category ⊺ equipped with an action of a commutative noetherian ring. This is used to establish a local-global principle and to develop a notion of stratification, for ⊺ and the cohomological functors on it, analogous to such concepts for compactly generated triangulated categories. 
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  2. ; ; (, Compositio Mathematica)
    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. 
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  3. ; ; (, Mathematische Annalen)
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  4. ; ; (, Journal of K-theory: K-theory and its Applications to Algebra, Geometry, and Topology)
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  5. ; (, Journal of Commutative Algebra)
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