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On R-triviality of F4

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Abstract

It is known that simple algebraic groups of type F4 defined over a field k are precisely the full automorphism groups of Albert algebras over k. We explore R-triviality for the algebraic group Aut(A) when A is an Albert algebra. In this paper, we consider the case when A arises from the first Tits construction. We prove that Aut(A) is R-trivial, in the sense of Manin.

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Acknowledgement

This work was partially funded by the DFG under Germany’s Excellence Strategy “EXC 2044-390685587, Mathematics Münster: Dynamics-Geometry-Structure”, when the author visited Math-Institute, Münster, in the summer of 2019. We thank Linus Kramer for his support. The author thanks Holger Petersson for some fruitful discussions at Hagen during the above period. We thank the referee for some very constructive suggestions that have improved the readability of the paper.

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  1. Theoretical Statistics and Mathematics Unit, Indian Statistical Institute, 8th Mile Mysore Road, Bangalore, 560059, India

    Maneesh Thakur

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Thakur, M. On R-triviality of F4. Isr. J. Math. 244, 145–161 (2021). https://doi.org/10.1007/s11856-021-2175-4

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  • DOI: https://doi.org/10.1007/s11856-021-2175-4

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