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A uniform bound on the Brauer groups of certain log K3 surfaces Bright, Martin


There has been much interest recently in bounding the Brauer groups of K3 surfaces over number fields. On the other hand, the arithmetic of integral points on log K3 surfaces appears to share some features with that of rational points on K3 surfaces. Some of the simplest examples of log K3 surfaces are the open surfaces obtained by starting with a projective del Pezzo surface and removing a smooth anticanonical divisor. We use Merel's boundedness of torsion on elliptic curves to prove boundedness of the Brauer groups of such log K3 surfaces over a number field. This is joint work with Julian Lyczak.

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