Abstract
Motivated by the André–Oort conjecture, Pila has proved an analogue of the Ax–Lindemann theorem for the uniformization of classical modular curves. In this paper, we establish a similar theorem in nonarchimedean geometry. Precisely, we give a geometric description of subvarieties of a product of hyperbolic Mumford curves such that the irreducible components of their inverse image by the Schottky uniformization are algebraic, in some sense. Our proof uses a -adic analogue of the Pila–Wilkie theorem due to Cluckers, Comte and Loeser, and requires that the relevant Schottky groups have algebraic entries.
Citation
Antoine Chambert-Loir. François Loeser. "A nonarchimedean Ax–Lindemann theorem." Algebra Number Theory 11 (9) 1967 - 1999, 2017. https://doi.org/10.2140/ant.2017.11.1967
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