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}
}
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