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Hearts of t-structures in the derived category of a commutative Noetherian ring. (English) Zbl 1390.18026
Let \(\mathcal{D}\) be a triangulated category. A t-structure in \(\mathcal{D}\) consists of a pair of full subcategories satisfying suitable axioms which ensure that their intersection is an abelian category, called the heart of the t-structure. For a commutative Noetherian ring \(R\), the authors prove that all compactly generated t-structures in the (unbounded) derived category \(\mathcal{D}(R)\) of \(R\) associated to a left bounded filtration by supports of Spec(\(R\)) have a heart which is a Grothendieck category, and describe those compactly generated t-structures whose heart is a module category. These results are used to deduce some geometric consequences for a compactly generated t-structure in the derived category \(\mathcal{D}(\mathbb{X})\) of an affine Noetherian scheme \(\mathbb{X}\).

MSC:
18E30 Derived categories, triangulated categories (MSC2010)
13D09 Derived categories and commutative rings
16E35 Derived categories and associative algebras
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