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Remarks on a conjecture of Chabauty

Author: Hatem Hamrouni
Journal: Proc. Amer. Math. Soc. 139 (2011), 1983-1987
MSC (2010): Primary 20E36, 20F16
Published electronically: November 10, 2010
MathSciNet review: 2775374
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Abstract: The Chabauty conjecture for connected nilpotent Lie groups has been proved by S. P. Wang. We show that one reasoning flaw has infiltrated the proof. We therefore give a new proof of the validity of Chabauty's conjecture in this setup. More generally, we shall prove that the Chabauty conjecture is true for rigid lattices and Zariski dense lattices of connected solvable Lie groups. In particular, the Chabauty conjecture holds for solvable Lie groups of $ (R)$-type.

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Hatem Hamrouni
Affiliation: Department of Mathematics, Faculty of Sciences at Sfax, University of Sfax, Route Soukra, B.P. 1171, 3000 Sfax, Tunisia

Keywords: Chabauty topology, solvable Lie group, discrete uniform subgroup.
Received by editor(s): May 27, 2010
Received by editor(s) in revised form: June 3, 2010
Published electronically: November 10, 2010
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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