Weak approximation for del Pezzo surfaces of low degree

Abstract: Conjecturally, the rational points of a del Pezzo surface over a number field are well-distributed among the local points over all but finitely completions of the ground field—that is, the surface satisfies weak weak approximation. However, describing the rational points becomes harder as the degree of the del Pezzo surface decreases. As such, many questions remain unanswered for del Pezzo surfaces of low degree. In this talk, I will report on recent joint work with Julian Demeio, in which we prove that del Pezzo surfaces of degrees 1 and 2 satisfy weak weak approximation, provided that we assume some additional geometric structure in the form of conic fibrations.

number theory

Audience: researchers in the topic

London number theory seminar

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