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Rational points on certain homogeneous varieties

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Abstract

Let L be a simply-connected simple connected algebraic group over a number field F, and H be a semisimple absolutely maximal connected F-subgroup of L. Let \(\Delta (H)\) be the image of H diagonally embedded in \(L^n\). Under a cohomological condition, we prove an asymptotic formula for the number of rational points of bounded height on projective equivariant compactifications of \(\Delta (H)\backslash L^n\) with respect to a balanced line bundle.

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Acknowledgements

The author would like to thank David Anderson and Alexander Gorodnik for helpful discussions. The author also would like to thank the referee for helpful suggestions.

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  1. Department of Mathematics, ETH Zürich, Rämistrasse 101, 8092, Zürich, Switzerland

    Pengyu Yang

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  1. Pengyu Yang
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Correspondence to Pengyu Yang.

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Yang, P. Rational points on certain homogeneous varieties. European Journal of Mathematics 9, 14 (2023). https://doi.org/10.1007/s40879-023-00599-z

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  • DOI: https://doi.org/10.1007/s40879-023-00599-z

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