Poincaré duality for the tropical Dolbeault cohomology of non-archimedean Mumford curves

Abstract

We calculate the tropical Dolbeault cohomology for the analytifications of P-1 and Mumford curves over non-archimedean fields. We show that the cohomology satisfies Poincare duality and behaves analogously to the cohomology of curves over the complex numbers. Further, we give a complete calculation of the dimension of the cohomology on a basis of the topology. (C) 2017 Elsevier Inc. All rights reserved.