I am looking for a version of Ehresmann's theorem for analytic manifolds over the $p$-adic numbers $\mathbb{Q}_p$ or, more generally, local fields. I follow the conventions from Serre's book "Lie algebras and Lie groups" concerning analytic manifolds over local fields.

Recall that Ehresmann's theorem states that a proper submersion between smooth manifolds is a locally trivial fibration.

Does a version of this hold for analytic manifolds over $\mathbb{Q}_p$? Namely, is a proper submerision between analytic manifolds over $\mathbb{Q}_p$ a locally trivial fibration?

I am looking for a version of Ehresmann's theorem for analytic manifolds over the $p$-adic numbers $\mathbb{Q}_p$ or, more generally, local fields. I follow the conventions from Serre's book "Lie algebras and Lie groups" concerning analytic manifolds over local fields.

Recall that Ehresmann's theorem states that a proper submersion between smooth manifolds is a locally trivial fibration.

Does a version of this hold for analytic manifolds over $\mathbb{Q}_p$? Namely, is a proper submersion between analytic manifolds over $\mathbb{Q}_p$ a locally trivial fibration?