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

Daniel Loughran; Ramin Takloo-Bighash; Sho Tanimoto

doi:10.1017/S1474748018000440

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

Daniel Loughran, Ramin Takloo-Bighash, Sho Tanimoto

Research output: Contribution to journal › Article › peer-review

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 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.

Original language	English
Pages (from-to)	1-41
Number of pages	41
Journal	Journal of the Institute of Mathematics of Jussieu
Early online date	29 Nov 2018
DOIs	https://doi.org/10.1017/S1474748018000440
Publication status	Published - 29 Nov 2018

Keywords

14F22
2010 Mathematics subject classification:
Primary 14G05
Secondary 11D45

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10.1017/S1474748018000440

https://arxiv.org/pdf/1705.09244.pdf

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KW - 14F22

KW - 2010 Mathematics subject classification:

KW - Primary 14G05

KW - Secondary 11D45

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ER -

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

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Keywords

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