Automorphisms of Frobenius twisted de Rham cohomology
Shizhang Li, Shubhodip Mondal
Published: 2025/9/21
Abstract
In this short paper, we prove that the moduli of automorphisms of Frobenius twisted de Rham cohomology functor is given by $\mathbb{G}_m$. Our method is to use the notion of $\mathbb{G}_a^{\mathrm{perf}}$-modules and its connection to the de Rham cohomology functor introduced in \cite{M22}. As an application of the induced $\mathbb{G}_m$-action, we reprove a result of Bhatt, Petrov, and Vologodsky on the decomposition of the Frobenius twisted de Rham complex.