## 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

### MSC:

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

Zbl 0528.14013
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