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arXiv · 2410.15125

Pullback Method with Applications to Severi--Brauer Fibrations

Mridul Biswas·Divyasree C Ramachandran·Biswanath Samanta
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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.

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Mridul Biswas, Divyasree C Ramachandran, Biswanath Samanta. 2024-10-19. Pullback Method with Applications to Severi--Brauer Fibrations. https://doi.org/10.1142/s1793042126500764

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