Submission date: 15 March 2011. Revised version with new title: 12 August 2011.

Abstract:

We give a positive answer to a question recently asked by A. Pillay and we give a new proof of the Mordell-Lang conjecture in positive characteristic in the case where the abelian variety is ordinary (theorem of Abramovich-Voloch). In essence, this new proof reduces the Mordell-Lang conjecture to the Manin-Mumford conjecture (in the ordinary case). This follows a suggestion of A. Pillay.

Mathematics Subject Classification: 11G10

Keywords and phrases:

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