A variational open image theorem in positive characteristic

TL;DR

This paper proves a variational open image theorem for Galois actions on the cohomology of smooth proper schemes over fields of positive characteristic, extending understanding of Galois representations in algebraic geometry.

Contribution

It establishes a new variational open adelic image theorem in positive characteristic, utilizing recent advances by Cadoret, Hui, and Tamagawa.

Findings

Proves a variational open adelic image theorem for Galois actions

Extends results to schemes over fields of positive characteristic

Utilizes recent foundational results in the field

Abstract

In this note we prove a variational open adelic image theorem for the Galois action on the cohomology of smooth proper $S$-schemes where $S$ is a smooth variety over a finitely generated field of positive characteristic. A central tool is a recent result of Cadoret, Hui and Tamagawa.