Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization Gross, Andreas Kaur, Inder Ulirsch, Martin Werner, Annette Let $A$ be an abelian variety with totally degenerate reduction over a non-Archimedean field. We describe the moduli space of semihomogeneous vector bundles on $A$ from the perspective of non-Archimedean uniformization and show that the essential skeleton may be identified with a tropical analogue of this moduli space. For $H=0$ our moduli space may be identified with the moduli space $M_{0,r}(A)$ of semistable vector bundles with vanishing Chern classes on $A$. In this case we construct a surjective analytic morphism from the character variety of the analytic fundamental group of $A$ onto $M_{0,r}(A)$, which naturally tropicalizes. One may view this construction as a non-Archimedean uniformization of $M_{0,r}(A)$. 2023 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_6501 https://ris.uni-paderborn.de/record/66309 Gross A, Kaur I, Ulirsch M, Werner A. Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization. <i>arXiv:231212980</i>. Published online 2023. doi:<a href="https://doi.org/10.1017/S2949764726100228">10.1017/S2949764726100228</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1017/S2949764726100228 info:eu-repo/semantics/altIdentifier/arxiv/2312.12980 info:eu-repo/semantics/closedAccess