Completing perfect complexes With appendices by Tobias Barthel and Bernhard Keller

Krause H (2020)
MATHEMATISCHE ZEITSCHRIFT.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch
 
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Abstract / Bemerkung
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 categories is compatible with the completion of derived categories. There are three appendices. The first one by Tobias Barthel discusses the completion of perfect complexes for ring spectra. The second one by Tobias Barthel and Henning Krause refines for a separated noetherian scheme the description of the bounded derived category of coherent sheaves as a completion. The final appendix by Bernhard Keller introduces the concept of a morphic enhancement for triangulated categories and provides a foundation for completing a triangulated category.
Stichworte
Completion; Cauchy sequence; Derived category; Triangulated category; Morphic enhancement; Perfect complex; Coherent ring; Noetherian scheme; Ring spectrum
Erscheinungsjahr
2020
Zeitschriftentitel
MATHEMATISCHE ZEITSCHRIFT
ISSN
0025-5874
eISSN
1432-1823
Page URI
https://pub.uni-bielefeld.de/record/2943302

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Krause H. Completing perfect complexes With appendices by Tobias Barthel and Bernhard Keller. MATHEMATISCHE ZEITSCHRIFT. 2020.
Krause, H. (2020). Completing perfect complexes With appendices by Tobias Barthel and Bernhard Keller. MATHEMATISCHE ZEITSCHRIFT. doi:10.1007/s00209-020-02490-z
Krause, H. (2020). Completing perfect complexes With appendices by Tobias Barthel and Bernhard Keller. MATHEMATISCHE ZEITSCHRIFT.
Krause, H., 2020. Completing perfect complexes With appendices by Tobias Barthel and Bernhard Keller. MATHEMATISCHE ZEITSCHRIFT.
H. Krause, “Completing perfect complexes With appendices by Tobias Barthel and Bernhard Keller”, MATHEMATISCHE ZEITSCHRIFT, 2020.
Krause, H.: Completing perfect complexes With appendices by Tobias Barthel and Bernhard Keller. MATHEMATISCHE ZEITSCHRIFT. (2020).
Krause, Henning. “Completing perfect complexes With appendices by Tobias Barthel and Bernhard Keller”. MATHEMATISCHE ZEITSCHRIFT (2020).