Azumaya objects in triangulated bicategories

作者：Johnson Niles^*

来源：Journal of Homotopy and Related Structures, 2014, 9(2): 465-493.

DOI：10.1007/s40062-013-0035-6

• Brauer group
• Ring spectrum
• Homotopical algebra

We introduce the notion of Azumaya object in general homotopy-theoretic settings. We give a self-contained account of Azumaya objects and Brauer groups in bicategorical contexts, generalizing the Brauer group of a commutative ring. We go on to describe triangulated bicategories and prove a characterization theorem for Azumaya objects therein. This theory applies to give a homotopical Brauer group for derived categories of rings and ring spectra. We show that the homotopical Brauer group of an Eilenberg-Mac Lane spectrum is isomorphic to the homotopical Brauer group of its underlying commutative ring. We also discuss tilting theory as an application of invertibility in triangulated bicategories.

• 出版日期2014