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Descent obstructions and Brauer–Manin obstruction in positive characteristic

Part of: Arithmetic algebraic geometry Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  01 June 2012

David Harari  and
José Felipe Voloch
David Harari
Affiliation:
Université Paris-Sud, Laboratoire de Mathématiques d’Orsay, Orsay Cedex, F-91405, France ([email protected])
José Felipe Voloch
Affiliation:
Department of Mathematics, University of Texas, Austin, TX 78712, USA ([email protected])
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Abstract

We prove that the Brauer–Manin obstruction is the only obstruction to the existence of integral points on affine varieties over global fields of positive characteristic $p$. More precisely, we show that the only obstructions come from étale covers of exponent $p$ or, alternatively, from flat covers coming from torsors under connected group schemes of exponent $p$.

Keywords

Artin–Schreier coveringBrauer–Manin obstructionGlobal field of positive characteristic

MSC classification

Secondary: 11G35: Varieties over global fields 14G17: Positive characteristic ground fields
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 12 , Issue 3 , July 2013 , pp. 545 - 551
Copyright
©Cambridge University Press 2012 

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