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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Good reduction of the Brauer-Manin obstruction


Authors: Jean-Louis Colliot-Thélène and Alexei N. Skorobogatov
Journal: Trans. Amer. Math. Soc. 365 (2013), 579-590
MSC (2010): Primary 14F22, 14G05, 11G35, 11G25
Published electronically: September 19, 2012
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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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Additional Information

Jean-Louis Colliot-Thélène
Affiliation: CNRS, UMR 8628, Mathématiques, Bâtiment 425, Université Paris-Sud, F-91405 Orsay, France
Email: jlct@math.u-psud.fr

Alexei N. Skorobogatov
Affiliation: Department of Mathematics, South Kensington Campus, Imperial College London, SW7 2BZ England, United Kingdom – and – Institute for the Information Transmission Problems, Russian Academy of Sciences, 19 Bolshoi Karetnyi, Moscow, 127994 Russia
Email: a.skorobogatov@imperial.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05556-5
PII: S 0002-9947(2012)05556-5
Received by editor(s): September 1, 2010
Published electronically: September 19, 2012
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.