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arXiv · 1706.07019

Index of fibrations and Brauer classes that never obstruct the Hasse principle

Masahiro Nakahara
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Abstract

Let $X$ be a smooth projective variety with a fibration into varieties that either satisfy a condition on representability of zero-cycles or that are torsors under an abelian variety. We study the classes in the Brauer group that never obstruct the Hasse principle for $X$. We prove that if the generic fiber has a zero-cycle of degree $d$ over the generic point, then the Brauer classes whose orders are prime to $d$ do not play a role in the Brauer--Manin obstruction. As a result we show that the odd torsion Brauer classes never obstruct the Hasse principle for del Pezzo surfaces of degree 2, certain K3 surfaces, and Kummer varieties.

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Masahiro Nakahara. 2017-06-21. Index of fibrations and Brauer classes that never obstruct the Hasse principle. https://arxiv.org/abs/1706.07019

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