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arXiv · 2104.12736

Deformation theory of perfect complexes and traces

Max Lieblich·Martin Olsson
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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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Max Lieblich, Martin Olsson. 2022-09-21. Deformation theory of perfect complexes and traces. https://doi.org/10.2140/akt.2022.7.651

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