P-adic heights and p-adic Hodge theory

Abstract

Using the theory of (ϕ, Γ)-modules and the formalism of Selmer complexes we construct the p-adic height pairing for p-adic representations with coefficients in an affinoid algebra over Q p. For p-adic representations that are potentially semistable at p, we relate our con-truction to universal norms and compare it to the p-adic height pairing of Nekovař. CONTENTS