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arXiv · 1106.2639

An application of generalized Matlis duality for quasi-\F-modules to the Artinianness of local cohomology modules

Danny Tobisch
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Abstract

We use a result of Hellus about generalized local duality to describe some generalized Matlis duals for certain quasi-\F-modules. Furthermore, we apply this description to obtain examples for non-artinian local cohomology modules by the theory of \F-modules. In particular, we get a new view on Hartshorne's counterexample for a conjecture by Grothendieck about the finiteness of $Hom_R(R/I,H^i_I(R))$ for a noetherian local Ring $R$ and an ideal $I \subseteq R$.

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Danny Tobisch. 2011-06-14. An application of generalized Matlis duality for quasi-\F-modules to the Artinianness of local cohomology modules. https://arxiv.org/abs/1106.2639

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