Zero-loci of Brauer group elements on semi-simple algebraic groups

2017/05/25 by Daniel Loughran, Loughran, Daniel, Ramin Takloo-Bighash +3 · 1 citation
Mathematics · #(secondary) #11D45 #14F22 #14G05 (primary) #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Finite Group Theory Research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1705.09244

openalex publication_date 2017/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the problem of counting the number of rational points of bounded height in the zero-loci of Brauer group elements on semi-simple algebraic groups over number fields. We obtain asymptotic formulae for the counting problem for wonderful compactifications using the spectral theory of automorphic forms. Applications include asymptotic formulae for the number of matrices over Q whose determinant is a sum of two squares. These results provide a positive answer to some cases of a question of Serre concerning such counting problems.

Citations

• Sur le nombre des points rationnels de hauteur borné des variétés algébriques

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