Diagonal del Pezzo surfaces of degree 2 with a Brauer-Manin obstruction
Linfoot Number Theory Seminar
2nd October 2024, 11:00 am – 12:00 pm
Fry Building, 2.04
Given a variety over the rationals, a natural question to ask is whether it has a rational point. If such a point exists, then the variety must have an adelic point. If the reverse implication holds, we say the variety satisfies the Hasse principle. It is well-known that the Hasse principle does not always hold, however it is conjectured by Colliot-Thélène that for rationally connected varieties the failure of the Hasse principle is explained by the Brauer-Manin obstruction. In this talk we will first discuss the Brauer-Manin obstruction (with specific focus on del Pezzo surfaces of degree 2). We will then discuss the difficulties of counting the Brauer-Manin obstruction on this family of surfaces, and the methods used to circumvent these difficulties.
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