Height Zeta Functions of Equivariant Compactifications of Unipotent Groups

DOI10.1002/cpa.21572zbMath1417.14002arXiv1501.02399OpenAlexW2962762634MaRDI QIDQ2802895

Yuri Tschinkel, Joseph A. Shalika

Publication date: 27 April 2016

Published in: Communications on Pure and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.02399

zbMATH Keywords

Manin's conjectureunipotent groupsequivariant compactifications

Mathematics Subject Classification ID

Other Dirichlet series and zeta functions (11M41) Zeta functions and related questions in algebraic geometry (e.g., Birch-Swinnerton-Dyer conjecture) (14G10) Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (7)

Distribution of rational points of bounded height on equivariant compactifications of \(\mathrm{PGL}_2\). I ⋮ Geometric consistency of Manin's conjecture ⋮ The Manin–Peyre conjecture for smooth spherical Fano varieties of semisimple rank one ⋮ Balanced line bundles on Fano varieties ⋮ On exceptional sets in Manin's conjecture ⋮ Campana points on biequivariant compactifications of the Heisenberg group ⋮ Motivic Euler Products and Motivic Height Zeta Functions

Cites Work

• Igusa integrals and volume asymptotics in analytic and adelic geometry
• Rational points of bounded height on Fano varieties
• Character formulas and spectra of compact nilmanifolds
• On the distribution of points of bounded height on equivariant compactifications of vector groups.
• Heights and Tamagawa measures on Fano varieties
• Decomposition of unitary representations defined by discrete subgroups of nilpotent groups
• Some Basic Theorems on Algebraic Groups
• Existence of minimal models for varieties of log general type
• Frobenius Reciprocity and Extensions of Nilpotent Lie Groups
• On Frobenius Reciprocity for Unipotent Algebraic Groups Over Q
• Decomposition of the L 2 -Space of a General Compact Nilmanifold
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