Arithmetic duality theorems in analytic geometry

Arithmetic duality theorems are in the center of many
constructions in Arithmetic. Among them: height pairings and
regulators. I will discuss what we know about arithmetic dualities for
rigid analytic varieties and explain these dualities in detail in the
simplest of cases: smooth Stein curves. This is based on a joint work
with Pierre Colmez and Sally Gilles.