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The Mordell-Lang question for endomorphisms of semiabelian varieties - MaRDI portal

The Mordell-Lang question for endomorphisms of semiabelian varieties (Q449716)

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scientific article; zbMATH DE number 6075051
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The Mordell-Lang question for endomorphisms of semiabelian varieties
scientific article; zbMATH DE number 6075051

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    The Mordell-Lang question for endomorphisms of semiabelian varieties (English)
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    31 August 2012
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    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.
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    \(p\)-adic exponential
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    Mordell-Lang conjecture
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    semiabelian varieties
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