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Autour d’une conjecture de Serge Lang. (Around a conjecture by Serge Lang). (English) Zbl 0638.14026
We study a conjecture of Serge Lang describing the intersection of an algebraic subvariety of an algebraic group \(G\) with a subgroup \(\Gamma\) of finite rank in \(G({\mathbb{C}})\). We prove the conjecture when \(\Gamma\) is the torsion subgroup of \(G\), extending previous result of Raynaud (case when \(G\) is an abelian variety) and Laurent (case when \(G\) is a linear torus). The method gives explicit results in terms of some Galois theoretic constant. We also prove some results and formulate some remarks on the general conjecture.
Reviewer: M.Hindry

14L10 Group varieties
20G15 Linear algebraic groups over arbitrary fields
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