Pullback Method with Applications to Severi--Brauer Fibrations

2024/10/19 by Mridul Biswas, Biswas, Mridul, Divyasree C Ramachandran +3
Mathematics · #Algebraic structures and combinatorial models #Analytic and geometric function theory #Finite Group Theory Research #math.AG #math.NT #msc:11G25 #msc:11G35 #msc:14F22 #msc:14G05 #msc:14G12 #msc:14J20

paper · pdf · doi:10.48550/arxiv.2410.15125

12 pages. Final version; to appear in Int.J.Number Theory

openalex publication_date 2024/10/19 · openalex created_date 2024/11/06 · arxiv created 2026/02/10 · arxiv updated 2026/07/30 · openalex updated_date 2026/07/31

Abstract

Given a variety with a suitable Brauer class, we present a general pullback construction that produces varieties that has Brauer--Manin obstruction to the existence of rational points. We then study Severi--Brauer fibrations and their Brauer groups without relying on explicit defining equations. As a key application, we show that there exist Severi--Brauer fibrations with index one that fails Hasse principle.

Related

• Brauer-Manin obstructions requiring arbitrarily many Brauer classes
• Brauer–Manin obstructions requiring arbitrarily many Brauer classes
• Rational points on varieties and the Brauer-Manin obstruction
• Severi-Brauer varieties; a geometric treatment
• Quartic del Pezzo surfaces with a Brauer group of order 4