The Coleman map for Hida families of GSp4

In this paper, we construct a Coleman map for ordinary Hida deformations associated to the symplectic group ${\rm GSp}_4$, which interpolates the dual exponential maps when arithmetic specializations of this family vary. The main result (Theorem 3.2) will play an important role in a forthcoming work by the authors discussing a conjecture on the existence of an Euler system which would give rise via our map to a three variable $p$-adic $L$-function.