Rational points on certain homogeneous varieties

2018/09/23 by Pengyu Yang, Yang, Pengyu
Mathematics · #14G05 (Primary) 11G50 (Secondary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1809.08512

openalex publication_date 2018/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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. Under a cohomological condition, we prove an asymptotic formula for the number of rational points of bounded height on projective equivariant compactifications of Δ(H)\backslash Lⁿ with respect to a balanced line bundle, where Δ(H) is the image of H diagonally embedded in Lⁿ.

Citations

• Rational points of bounded height on Fano varieties

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