Nonexistence of quadratic points on del Pezzo surfaces of degree 4 over global function fields

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• Katerina Santicola (University of Bath)
• Tuesday 21 October 2025, 14:30-15:30
• MR13.

If you have a question about this talk, please contact Bence Hevesi.

Colliot-Thélène recently asked whether every del Pezzo surface of degree 4 (dP4) has a quadratic point over a $C_2$ field. This question has counterexamples over $C_3$ fields and a positive result over $C_1$ fields but remained open for all $C_2$ fields. Last year Creutz and Viray built an infinite family of dP4s without quadratic points over $\mathbb{Q}$. In work in progress, we follow their method to construct an infinite family of dP4s with a Brauer-Manin obstruction to a quadratic point over $\mathbb{F}_p(t)$ for all $p\neq 2$, thus answering Colliot-Thélène’s question in the negative. This is joint work with Giorgio Navone, Harry Shaw and Dr Haowen Zhang.

This talk is part of the Number Theory Seminar series.

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