On $R$-triviality of $F_4$-II

Abstract

Simple algebraic groups of type $F_4$ defined over a field $k$ are the full automorphism groups of Albert algebras over $k$. Let $A$ be an Albert algebra over a field $k$ of arbitrary characteristic. We prove that there is an isotope $A^{(v)}$ of $A$ such that the group $\text{Aut}(A^{(v)})$ is $R$-trivial, in the sense of Manin.

arXiv commentarXiv admin note: substantial text overlap with arXiv:1912.01433, arXiv:1911.04976, arXiv:1704.07811