Azumaya representation schemes

We extend Grothendieck topologies on commutative algebras to the category of all Azumaya algebras and we show that the functor assigning to an Azumaya algebra A the set of all algebra maps R→A from a fixed C-algebra R, is a sheaf for all such Grothendieck topologies coarser than the maximal flat topology. We construct Azumaya representation schemes representing algebra maps from R to a fixed Azumaya algebra A, which is relevant in the study of the representation stack [repn(R)/PGLn]. Finally, we describe the related quotient stack [repα(R)/PGL(α)] in terms of twisted representations of quivers.

Publication year:2016

Keywords:A3 Journal article

Accessibility:Open