# Completing perfect complexes

@article{Krause2020CompletingPC, title={Completing perfect complexes}, author={Henning Krause}, journal={Mathematische Zeitschrift}, year={2020}, pages={1-41} }

This note proposes a new method to complete a triangulated category, which is based on the notion of a Cauchy sequence. We apply this to categories of perfect complexes. It is shown that the bounded derived category of finitely presented modules over a right coherent ring is the completion of the category of perfect complexes. The result extends to non-affine noetherian schemes and gives rise to a direct construction of the singularity category. The parallel theory of completion for abelian…

## 12 Citations

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We give two proofs of the following theorem and a partial generalization: if a finite‐dimensional algebra A is derived equivalent to a smooth projective scheme, then any derived equivalence between A…

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Abstract For a finite dimensional algebra A, the bounded homotopy category of projective A-modules and the bounded derived category of A-modules are dual to each other via certain categories of…

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We study rational curves on smooth complex Calabi--Yau threefolds via noncommutative algebra. By the general theory of derived noncommutative deformations due to Efimov, Lunts and Orlov, the…

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Given a tilting object of the derived category of an abelian category of finite global dimension, we give (under suitable finiteness conditions) a bound for the global dimension of its endomorphism…

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- Mathematics, PsychologyProceedings of the Royal Society of Edinburgh: Section A Mathematics
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For each recollement of triangulated categories, there is an epivalence between the middle category and the comma category associated with a triangle functor from the category on the right to the…

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