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- W2949086104 abstract "We study the tropical Dolbeault cohomology of non-archimedean curves as defined by Chambert-Loir and Ducros. We give a precise condition for when this cohomology satisfies Poincare duality. The condition is always satisfied when the residue field of the non-archimedean base field is the algebraic closure of a finite field. We also show that for curves over fields where the residue field is the field of complex numbers, the tropical (1,1)-Dolbeault cohomology can be infinite dimensional. Our main new ingredient is an exponential type sequence that relates tropical Dolbeault cohomology to the cohomology of the sheaf of harmonic functions. As an application of our Poincare duality result, we calculate the dimensions of the tropical Dolbeault cohomology, called tropical Hodge numbers, for (open subsets of) curves." @default.
- W2949086104 created "2019-06-27" @default.
- W2949086104 creator A5042994630 @default.
- W2949086104 date "2017-06-19" @default.
- W2949086104 modified "2023-09-27" @default.
- W2949086104 title "Tropical Hodge numbers of non-archimedean curves" @default.
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- W2949086104 hasPublicationYear "2017" @default.
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