Denis's Mordell–Lang conjecture for Drinfeld modules

Let KK be a field extension of Fp(t){\mathbb F}_p(t), let Φ\Phi be a Drinfeld module of generic characteristic over KK, let XGagX\subseteq {\mathbb G}_a^g be a subvariety, and let ΓKg\Gamma\subseteq K^g be a finitely generated Φ(R)\Phi(R)-module, where R=Fp[t]R={\mathbb F}_p[t]. Denis's Mordell–Lang conjecture. The intersection X(K)ΓX(K)\cap\Gamma is a finite union of translates of Φ(R)\Phi(R)-submodules of Γ\Gamma. This is the Drinfeld-module analogue of the Mordell–Lang conjecture for abelian varieties. The paper presents it as the motivation for its local-to-global results, but the conjecture remains open in the stated generality.

Sources & referencesView supporting material

Primary source

Dragos Ghioca and Thomas Scanlon, “Algebraic equations on the adelic closure of a Drinfeld module”, arXiv:1012.1825 (2010).

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