Work

Transcendental Brauer groups of cubic generalised Kummer surfaces

Year: 2026

Type: article

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

Source: Mathematical Proceedings of the Cambridge Philosophical Society

DOI: 10.1017/s0305004126102199

Author: GIORGIO NAVONE

Institution: University College London

Language: English

Topic: Algebraic Geometry and Number Theory

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,550

Funders: University College London, Engineering and Physical Sciences Research Council