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arXiv · 2001.09749

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

Maneesh Thakur
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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 $\text{\bf Aut}(A^{(v)})$ is $R$-trivial, in the sense of Manin.

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Maneesh Thakur. 2020-01-02. On $R$-triviality of $F_4$-II. https://arxiv.org/abs/2001.09749

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