duality theory of p-adic hopf algebras

We show the monoidal functoriality of schikhof duality, and cultivate new duality theory of p-adic hopf algebras. through the duality, we introduce two sorts of p-adic pontryagin dualities. one is a duality between discrete abelian groups and affine formal group schemes of specific type, and the other one is a duality between profinite abelian groups and analytic groups of specific type. we extend amice transform to a p-adic fourier transform compatible with the second p-adic pontryagin duality. as applications, we give explicit presentations of a universal family of irreducible p-adic unitary banach representations of the open unit disc of the general linear group and its q-deformation in the case of dimension 2.