Functoriality, Smith theory, and the Brauer homomorphism


If $\sigma$ is an automorphism of order $p$ of the semisimple group $\mathbf{G}$, there is a natural correspondence between $\mathrm{mod}p$ cohomological automorphic forms on $\mathbf{G}$ and $\mathbf{G}^{\sigma}$. We describe this correspondence in the global and local settings.


David Treumann

Boston College, Chestnut Hill, MA

Akshay Venkatesh

Stanford University, Stanford, CA