Mordell exceptional locus for subvarieties of the additive group

We define the Mordell exceptional locus $Z(V)$ for affine varieties $V\subset\bG_a^g$ with respect to the action of a product of Drinfeld modules on the coordinates of $\bG_a^g$. We show that $Z(V)$ is a closed subset of $V$. We also show that there are finitely many maximal algebraic $\phi$-modules whose translates lie in $V$. Our results are motivated by Denis-Mordell-Lang conjecture for Drinfeld modules.

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Published 1 January 2008