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arXiv · 2506.16372

Transcendental Brauer groups of cubic generalised Kummer surfaces

Giorgio Navone
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Abstract

Given a cubic curve $C$ over a number field, we consider the K3 surface $Y_C$ constructed as the minimal desingularisation of the quotient of $C \times C$ by an automorphism of order 3. We relate the transcendental Brauer groups of $Y_C$ and $C \times C$, allowing us to explicitly compute the former group in the case of a diagonal cubic curve defined over $\mathbb{Q}$. We obtain conjectural insight on the existence of Galois cubic points over $\mathbb{Q}$ for everywhere locally soluble diagonal cubic curves.

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BibTeXRIS

Giorgio Navone. 2025-06-19. Transcendental Brauer groups of cubic generalised Kummer surfaces. https://arxiv.org/abs/2506.16372

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