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arXiv · 1612.01889

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

Philipp Jell·Veronika Wanner
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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.

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Philipp Jell, Veronika Wanner. 2017-12-29. Poincaré duality for tropical Dolbeault cohomology of non-archimedean Mumford curves. https://doi.org/10.1016/j.jnt.2017.11.004

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