### Weak approximation for del Pezzo surfaces of low degree

Heilbronn Number Theory Seminar

29th September 2021, 4:00 pm – 5:00 pm

Online,

Work of Iskovskih shows that any geometrically rational surface is birational to a conic bundle or a del Pezzo surface. In this talk, we focus on surfaces in the intersection of these two families through the lens of weak approximation. In joint work in progress with Julian Demeio, we show that a general del Pezzo surface of degree one or two with a conic fibration satisfies weak weak approximation, or weak approximation away from finitely many places. We utilise a result of Denef connecting arithmetic surjectivity (surjectivity on local points at all but finitely many places) with the scheme-theoretic notion of splitness.

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