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arXiv · 2607.26915

Splitting Brauer classes by genus one curves over number fields

Benjamin Antieau·Asher Auel·Federico Scavia
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Abstract

We prove that every Severi-Brauer variety of dimension at least two over a number field contains a twisted elliptic normal curve. Consequently, every Brauer class over a number field is split by a genus one curve. We prove this using the fibration method, by showing that the rational points on a smooth compactification of the Hilbert scheme of twisted elliptic normal curves are dense in its Brauer-Manin set.

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Benjamin Antieau, Asher Auel, Federico Scavia. 2026-07-29. Splitting Brauer classes by genus one curves over number fields. https://arxiv.org/abs/2607.26915

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