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Deformation theory of perfect complexes and traces

Max Lieblich and Martin Olsson

Vol. 7 (2022), No. 4, 651–694
DOI: 10.2140/akt.2022.7.651
Abstract

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 K-theory and higher category theory.

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Keywords
perfect complexes, deformation theory
Mathematical Subject Classification
Primary: 14C35
Milestones
Received: 23 July 2021
Revised: 26 August 2022
Accepted: 13 September 2022
Published: 15 March 2023
Authors
Max Lieblich
Department of Mathematics
University of Washington
Seattle, WA
United States
Martin Olsson
Department of Mathematics
University of California
Berkeley, CA
United States