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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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