### Semi-integral points and quadrics

Heilbronn Number Theory Seminar

16th March 2022, 4:00 pm – 5:00 pm

Fry Building, 2.04

In this talk I will discuss two notions of semi-integral points, termed Campana points and Darmon points, on Campana orbifolds associated to quadric hypersurfaces. In a joint work with Masahiro Nakahara and Sam Streeter we show that Campana weak approximation is satisfied for all quadric hypersurfaces with a weighted hyperplane section as orbifold divisor. We also develop a version of the Brauer-Manin obstruction for semi-integral points which allows us to study how often quadrics fail the Hasse principle for semi-integral points.

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