Autour d'une conjecture de Serge Lang. (Around a conjecture by Serge Lang)
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.
algebraic subvariety of an algebraic group
scientific article; zbMATH DE number 4040085
scientific article