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The category $\big[{\mathcal T}^c\big]^{\text{op}}$ as functors on ${\mathcal T}^b_c$
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We revisit an old assertion due to Rouquier, characterizing the perfect complexes as bounded homological functors on the bounded complexes of coherent sheaves. The new results vastly generalize the old statement---first of all the ground ring is not restricted to be a field, any commutative, noetherian ring will do. But the generalization goes further, to the abstract world of approximable triangulated categories.
Forward citations
Cited by 2 Pith papers
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Deformations of triangulated categories with t-structures via derived injectives
Bounded t-deformations of a bounded t-dg-category are equivalent to dg-deformations of its category of derived injectives, and HH^n classifies them for n at least 2.
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Approximable Triangulated Categories and Reflexive DG-categories
A locally finite approximable DG-category with a strong generator inside its finitely valued modules is finite-reflexive; this yields reflexivity for proper schemes, Azumaya algebras, and proper connective DG-algebras.
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