Galois equations on torsion points and the Tate-Voloch conjecture on p-adic fields

The Tate-Voloch conjecture is a statement about p-adic distance from torsion points to subvarieties in a semi-abelian variety defined over C_p. The use of Galois equations on torsion points by Pink and Rossler to prove the Manin-Mumford conjecture can be adapted to prove that conjecture in the case where both the semi-abelian variety and its subvariety are defined over a finite extension of Q_p.In this talk, we will present such a proof, and try to give an insight on how this proof differs from the model-theoretic one given by Scanlon.