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Deformation theory of
perfect complexes and traces
Max Lieblich and Martin Olsson |
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Vol. 7 (2022), No. 4, 651–694
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DOI: 10.2140/akt.2022.7.651
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Abstract |
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We show that the deformation theory of a perfect complex and that of its determinant are related by the trace map, in a general setting of sheaves on a site. The key technical step, in passing from the setting of modules over a ring where one has global resolutions to the general setting, is achieved using -theory and higher category theory. |
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Keywords
perfect complexes, deformation theory
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Mathematical Subject Classification
Primary: 14C35
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Milestones
Received: 23 July 2021
Revised: 26 August 2022
Accepted: 13 September 2022
Published: 15 March 2023
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Authors |
| Max Lieblich | |
| Department of Mathematics University of Washington Seattle, WA United States |
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| Martin Olsson | |
| Department of Mathematics University of California Berkeley, CA United States |
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