The finitely generated Drinfeld-module Siegel conjecture for integral points

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Let KK be a global function field, let MKM_K be its set of places, let S⊆MKS\subseteq M_K be finite, and let ϕ\phi be a Drinfeld module over KK. A point γ\gamma is SS-integral for α\alpha if it satisfies the corresponding SS-integrality condition relative to α\alpha. The finitely generated Drinfeld-module Siegel conjecture. Let α\alpha be any point in Ga(K‾)\mathbb{G}_a(\overline K), and let Γ\Gamma be any finitely generated ϕ\phi-submodule of Ga(K‾)\mathbb{G}_a(\overline K). Then there are finitely many γ∈Γ\gamma\in\Gamma such that γ\gamma is SS-integral for α\alpha.

This asks for a finiteness theorem extending the preceding corollary from torsion points to finitely generated Drinfeld-module submodules. The source presents it as a further question and gives no resolution status.

References

Primary source

Dragos Ghioca and Thomas J. Tucker, “Equidistribution and integral points for Drinfeld modules”, arXiv:math/0609120 (2007).

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