Corpus ID: 199452670

# Azumaya geometry and representation stacks

@article{Hemelaer2016AzumayaGA,
title={Azumaya geometry and representation stacks},
author={Jens Hemelaer and L. L. Bruyn},
journal={arXiv: Rings and Algebras},
year={2016}
}
• Published 2016
• Mathematics
• arXiv: Rings and Algebras
We develop Azumaya geometry, which is an extension of classical affine geometry to the world of Azumaya algebras, and package the information contained in all quotient stacks $[\mathrm{rep}_n R\,/\,\mathrm{PGL}_n]$ into a presheaf $\mathrm{Rep}_R$ on it. We show that the classical etale and Zariski topologies extend to Grothendieck topologies on Azumaya geometry in uncountably many ways, and prove that $\mathrm{Rep}_R$ is a sheaf for all of them. The restriction to a specific Azumaya algebra \$A… Expand