# Non-invariance of the Brauer-Manin obstruction for surfaces

@inproceedings{Wu2021NoninvarianceOT, title={Non-invariance of the Brauer-Manin obstruction for surfaces}, author={Han Wu}, year={2021} }

In this paper, we study the properties of weak approximation with BrauerManin obstruction and the Hasse principle with Brauer-Manin obstruction for surfaces with respect to field extensions of number fields. We assume a conjecture of M. Stoll. For any nontrivial extension of number fields L/K, we construct two kinds of smooth, projective, and geometrically connected surfaces defined over K. For the surface of the first kind, it has a K-rational point, and satisfies weak approximation with…

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