# Completing perfect complexes

@article{Krause2020CompletingPC,
title={Completing perfect complexes},
author={Henning Krause},
journal={Mathematische Zeitschrift},
year={2020},
pages={1-41}
}
• H. Krause
• Published 28 May 2018
• Mathematics
• Mathematische Zeitschrift
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…
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