Any two symplectic forms on a p-adic analytic manifold are locally isomorphic, and second-countable p-adic analytic symplectic manifolds are classified by their p-adic volume.
Cannas da Silva:Lectures on Symplectic Geometry.Lecture Notes in Math., 1764, Springer- Verlag, Berlin, 2001
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Darboux's Theorem in $p$-adic symplectic geometry
Any two symplectic forms on a p-adic analytic manifold are locally isomorphic, and second-countable p-adic analytic symplectic manifolds are classified by their p-adic volume.