p-adic periods and connectivity of the motivic Hopf algebra in positive characteristic

I will recall the construction of a new Weil cohomology theory whose coefficient ring consists of abstract p-adic periods. I will then use this new Weil cohomology theory to prove that the motivic Hopf algebras associated to the classical Weil cohomology theories are connective. (This is new only when the base field has positive characteristic, and the proof proceeds by reducing to the characteristic zero case.)