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arXiv · 1903.02607

Local cohomology in Grothendieck categories

Fatemeh Savoji·Reza Sazeedeh
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Abstract

Let $\mathcal{A}$ be a locally noetherian Grothendieck category. In this paper we define and study the section functor on $\mathcal{A}$ with respect to an open subset of ASpec$\mathcal{A}$. Next we define and study local cohomology theory in $\mathcal{A}$ in terms of the section functors. Finally we study abstract local cohomology functor on the derived category $\mathcal{D}^+(\mathcal{A})$.

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Fatemeh Savoji, Reza Sazeedeh. 2019-03-06. Local cohomology in Grothendieck categories. https://arxiv.org/abs/1903.02607

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