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

Abstract

Let U be the complement of a smooth anticanonical divisor in a del Pezzo surface of degree at most 7 over a number field k. We show that there is an effective uniform bound for the size of the Brauer group of U in terms of the degree of k.

arXiv commentMinor improvements to presentation

References in corpus (6)

• Groupe de Brauer et points entiers de deux familles de surfaces cubiques affines
• On the Brauer group of diagonal quartic surfaces
• Bornes effectives pour la torsion des courbes elliptiques sur les corps de nombres
• Finiteness theorems for K3 surfaces and abelian varieties of CM type
• Transcendental Brauer groups of products of CM elliptic curves
• Effective bounds for Brauer groups of Kummer surfaces over number fields

Cited by in corpus (1)

• Integral Hasse principle and strong approximation for Markoff surfaces