2012/09/02 by Tim Browning, T. D. Browning, Lilian Matthiesen +5
Engineering · Mathematics · #11G35 #14D10 (Secondary) #14G05 (Primary) 11B30 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Number Theory (math.NT) #math.AG #math.NT #msc:11B30 #msc:11G35 #msc:14D10 #msc:14G05
paper · pdf · doi:10.48550/arxiv.1209.0207
18 pages; shorter proof of Theorem 1.4
openalex publication_date 2012/09/02 · arxiv created 2013/06/14 · arxiv updated 2013/06/17 · openalex created_date 2022/08/15 · openalex updated_date 2026/07/28
For any pencil of conics or higher-dimensional quadrics over the rationals, with all degenerate fibres defined over the rationals, we show that the Brauer-Manin obstruction controls weak approximation. The proof is based on the Hasse principle and weak approximation for some special intersections of quadrics, which is a consequence of recent advances in additive combinatorics.