Pullback Method with Applications to Severi--Brauer Fibrations

Fuente: arXiv
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Main Authors: Biswas, Mridul, Ramachandran, Divyasree C, Samanta, Biswanath
Format: Preprint
Published: 2024
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_version_ 1866911435785764864
author Biswas, Mridul
Ramachandran, Divyasree C
Samanta, Biswanath
author_facet Biswas, Mridul
Ramachandran, Divyasree C
Samanta, Biswanath
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2410_15125
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Pullback Method with Applications to Severi--Brauer Fibrations
Biswas, Mridul
Ramachandran, Divyasree C
Samanta, Biswanath
Number Theory
Algebraic Geometry
Primary 14G05, Secondary 14G12, 11G35, 14J20, 11G25, 14F22
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.
title Pullback Method with Applications to Severi--Brauer Fibrations
topic Number Theory
Algebraic Geometry
Primary 14G05, Secondary 14G12, 11G35, 14J20, 11G25, 14F22
url https://arxiv.org/abs/2410.15125