Higher Brauer groups and higher Azumaya algebras

Abstract: Let X be some scheme. We are all familiar with the fact that classes in H^1(X,G_m) correspond to line bundles, or invertible sheaves. Most of us have also seen the interpretation of H^2(X,G_m) as Azumaya algebras, which are invertible bundles up to Morita equivalence. This raises the question: what about H^3, or H^4, or H^n? Can they be interpreted as some kind of invertible objects over X? For H^3, the answer turns out to be yes, and we will describe objects we call 2-Azumaya algebras which provide such an interpretation.

algebraic geometrynumber theory

Audience: researchers in the topic

Leiden Algebra, Geometry, and Number Theory Seminar