Brauer-Manin obstruction for symmetric powers

Yang Cao; Lin Zhou

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arXiv · 2610.23430

Brauer-Manin obstruction for symmetric powers

Yang Cao·Lin Zhou

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Abstract

For a quasi-projective smooth geometrically integral variety $X$ over a number field, we prove that the Brauer-Manin obstruction for its symmetric powers coincides with the obstruction coming from $X$. As a consequence, Brauer-Manin obstruction for the symmetric powers cannot provide new cohomological obstruction to weak approximation of zero-cycles for $X$. The key intermediate ingredients are a Dold-Thom type result for Brauer groups and a precise descent formula for adelic points.

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Yang Cao, Lin Zhou. 2026-10-16. Brauer-Manin obstruction for symmetric powers. https://arxiv.org/abs/2610.23430

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