Rational points on compactifications of semi-simple algebraic groups

Abstract

We prove Manin's conjecture concerning the distribution of rational points of bounded height, and its refinement by Peyre, for wonderful compactifications of semi-simple algebraic groups over number fields. The proof proceeds via the study of the associated height zeta function and its spectral expansion.

References in corpus (6)

• Manin's conjecture for toric varieties
• Tamagawa numbers of polarized algebraic varieties
• Rational Points of Bounded Height on Compactifications of Anisotropic Tori
• Functorial products for $G{L}_2\times G{L}_3$ and the symmetric cube for $G{L}_2$
• Height zeta functions of equivariant compactifications of the Heisenberg group
• Fonctions zêta des hauteurs des espaces fibrés

Cited by in corpus (12)

• Integral points on symmetric varieties and Satake compatifications
• On the wonderful compactification
• Integral points of bounded height on toric varieties
• Campana points of bounded height on vector group compactifications
• Campana points on biequivariant compactifications of the Heisenberg group
• Asymptotic behaviour of rational curves
• Log canonical thresholds on group compactifications
• Manin's conjecture for certain spherical threefolds
• Distribution of orders in number fields
• R-equivalence on group schemes
• An equivariant compactification for adjoint reductive group schemes
• Asymptotic growth of translation-dilation orbits