Good reduction of the Brauer–Manin obstruction

Colliot-Thélène, Jean-Louis; Skorobogatov, Alexei

doi:10.1090/S0002-9947-2012-05556-5

Good reduction of the Brauer–Manin obstruction
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by Jean-Louis Colliot-Thélène and Alexei N. Skorobogatov PDF

Trans. Amer. Math. Soc. 365 (2013), 579-590 Request permission

Abstract:

For a smooth and projective variety over a number field with torsion-free geometric Picard group and finite transcendental Brauer group we show that only the archimedean places, the primes of bad reduction and the primes dividing the order of the transcendental Brauer group can turn up in the description of the Brauer–Manin set.

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