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arXiv · 1602.03226

Extended Local Cohomology and Local Homology

Sean Sather-Wagstaff·Richard Wicklein
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Abstract

We present an in-depth exploration of the module structures of local (co)homology modules (moreover, for complexes) over the completion $\widehat R^{\mathfrak a}$ of a commutative noetherian ring $R$ with respect to a proper ideal $\mathfrak a$. In particular, we extend Greenlees-May Duality and MGM Equivalence to track behavior over $\widehat R^{\mathfrak a}$, not just over $R$. We apply this to the study of two recent versions of homological finiteness for complexes, and to certain isomorphisms, with a view toward further applications. We also discuss subtleties and simplifications in the computations of these functors.

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Sean Sather-Wagstaff, Richard Wicklein. 2016-02-10. Extended Local Cohomology and Local Homology. https://arxiv.org/abs/1602.03226

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