Abelian tropical covers Len, Yoav Ulirsch, Martin Zakharov, Dmitry Let $\mathfrak{A}$ be a finite abelian group. In this article, we classify harmonic $\mathfrak{A}$-covers of a tropical curve $Γ$ (which allow dilation along edges and at vertices) in terms of the cohomology group of a suitably defined sheaf on $Γ$. We give a realizability criterion for harmonic $\mathfrak{A}$-covers by patching local monodromy data in an extended homology group on $Γ$. As an explicit example, we work out the case $\mathfrak{A}=\mathbb{Z}/p\mathbb{Z}$ and explain how realizability for such covers is related to the nowhere-zero flow problem from graph theory. 2019 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/66325 Len Y, Ulirsch M, Zakharov D. Abelian tropical covers. <i>arXiv:190604215</i>. Published online 2019. doi:<a href="https://doi.org/10.1017/S0305004123000518">10.1017/S0305004123000518</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1017/S0305004123000518 info:eu-repo/semantics/altIdentifier/arxiv/1906.04215 info:eu-repo/semantics/closedAccess