Quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ without quadratic points
Abstract
We construct an infinite family of quartic del Pezzo surfaces over $\mathbb{F}_p(t)$ with no quadratic points, for all primes $p\neq 2$. This answers a question of Colliot--Thélène, Creutz and Viray in the negative, which asks whether every quartic del Pezzo surface has quadratic points over $C_2$ fields. We exhibit a Brauer--Manin obstruction on the variety parametrising lines associated to the quartic del Pezzo surface.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Advanced Algebra and Geometry
Analytic Number Theory Research
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 25 February 2026
- Language
- EN
- Document type
- Preprint