Pullback Method with Applications to Severi--Brauer Fibrations
Number Theory
2026-02-11 v4 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2410.15125,
title = {Pullback Method with Applications to Severi--Brauer Fibrations},
author = {Mridul Biswas and Divyasree C Ramachandran and Biswanath Samanta},
journal= {arXiv preprint arXiv:2410.15125},
year = {2026}
}
Comments
12 pages. Final version; to appear in Int.J.Number Theory