What type of study is this?

This is a Quantitative Study study.

October 20, 2025Open Access

Transcendental Brauer groups of cubic generalised Kummer surfaces

Key Points

The study finds a relationship between the transcendental Brauer groups of K3 surfaces and cubic curves, enhancing our understanding.
Key evidence includes calculations showing explicit computation of Brauer groups for diagonal cubic curves over rational numbers.
Approach utilized includes examining cubic curves, specifically the K3 surface formed through the desingularization process, allowing for deeper insights.
These findings may suggest potential directions for exploring Galois cubic points in cubic curves, indicating new areas for further research.

Abstract

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

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Cite This Study

Giorgio Navone (Thu,) studied this question.

synapsesocial.com/papers/68f6196ee0bbbc94fac3623b https://doi.org/https://doi.org/10.48550/arxiv.2506.16372

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