Poincaré duality for tropical Dolbeault cohomology of non-archimedean Mumford curves
arXiv:1612.01889 · doi:10.1016/j.jnt.2017.11.004
Abstract
We calculate the tropical Dolbeault cohomology for the analytifications of the projective line and Mumford curves over non-archimedean fields. We show that the cohomology satisfies Poincaré 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.
To appear in Journal of Number Theory. 22 pages