The trace morphism and Poincaré duality in p-adic non-archimedean geometry

I will explain a construction of the trace morphism for smooth morphism of analytic adic spaces. Then I will explain how one can use this trace to prove various Poincare Duality type results. In particular, I will discuss a new easy proof of Poincare Duality for F_p-cohomology groups of smooth proper p-adic rigid-analytic spaces and an appropriate generalization of this result to arbitrary proper morphisms.