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The Mordell-Lang question for endomorphisms of semiabelian varieties. (English. French summary) Zbl 1256.14046

The Mordell-Lang conjecture (which is proved) states that for a finitely generated subgroup \(\Gamma\) and a subvariety \(V\cap G\) of a semiabelian \(G(C)\) the intersection \(V\cap\Gamma\) lies in finitely many translates \(V_\alpha\subset V\) of subgroups. The paper under review replaces \(\Gamma\) by \(\Phi^{n_1}_1\cdots \Phi^{n_r}_r(\alpha)\), where \(\alpha\) is a point and the \(\Phi_i\) are commuting endomorphisms of \(G\). Under some technical assumptions an analogue of Mordell-Lang holds. The proof uses \(p\)-adic methods.

MSC:

14L10 Group varieties
37P55 Arithmetic dynamics on general algebraic varieties
11G20 Curves over finite and local fields
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References:

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