Deformation theory of perfect complexes and traces

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.

36 pages, final version, to appear in Annals of K-Theory

References in corpus (6)

• Higher Topos Theory
• On the algebraic K-theory of higher categories
• Universality of multiplicative infinite loop space machines
• Enhanced six operations and base change theorem for higher Artin stacks
• Algebraic K-theory and descent for blow-ups
• Modules over algebraic cobordism