A formal density theorem says that, under a Newton-Hodge irreducibility condition, deformations of a mod p point with large p-adic monodromy are open dense in every p-adic neighborhood.
[Zha0501] Shou-Wu Zhang, Equidistribution of cm-points on quaternion shimura varieties , International Mathematics Research Notices 2005 (200501), no
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Towards a p-adic nowhere density conjecture of Hecke Orbits
A formal density theorem says that, under a Newton-Hodge irreducibility condition, deformations of a mod p point with large p-adic monodromy are open dense in every p-adic neighborhood.