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arXiv · 1803.07546

On generalized Hartshorne's conjecture and local cohomology modules

Thiago Henrique Freitas·Victor Hugo Jorge Pérez·Liliam Carsava Merighe
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Abstract

Let $\mathfrak{a}$ denote an ideal of a commutative Noetherian ring $R$. Let $M$ and $N$ be two $R$-modules. In this paper, we give partial answers on the extension of Hartshorne's conjecture about the cofiniteness of torsion and extension functors. For this purpose, we study the cofiniteness of the generalized local cohomology module $H^{i}_{\mathfrak{a}}(M, N)$ for a new class of modules, called $\mathfrak{a}$-weakly finite modules, in the local and non-local case. Furthermore, we derive some results on attached primes of top generalized local cohomology modules.

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Thiago Henrique Freitas, Victor Hugo Jorge Pérez, Liliam Carsava Merighe. 2018-03-20. On generalized Hartshorne's conjecture and local cohomology modules. https://arxiv.org/abs/1803.07546

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