article Andreas Gross author Inder Kaur author Martin Ulirsch author 114697 Annette Werner author 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 eng 2312.1298010.1017/S2949764726100228 @article{Gross_Kaur_Ulirsch_Werner_2023, title={Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization}, DOI={<a href="https://doi.org/10.1017/S2949764726100228">10.1017/S2949764726100228</a>}, journal={arXiv:2312.12980}, author={Gross, Andreas and Kaur, Inder and Ulirsch, Martin and Werner, Annette}, year={2023} } 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> Gross, Andreas, et al. “Semi-Homogeneous Vector Bundles on Abelian Varieties: Moduli Spaces and Their Tropicalization.” <i>ArXiv:2312.12980</i>, 2023, doi:<a href="https://doi.org/10.1017/S2949764726100228">10.1017/S2949764726100228</a>. A. Gross, I. Kaur, M. Ulirsch, A. Werner, ArXiv:2312.12980 (2023). Gross, Andreas, Inder Kaur, Martin Ulirsch, and Annette Werner. “Semi-Homogeneous Vector Bundles on Abelian Varieties: Moduli Spaces and Their Tropicalization.” <i>ArXiv:2312.12980</i>, 2023. <a href="https://doi.org/10.1017/S2949764726100228">https://doi.org/10.1017/S2949764726100228</a>. A. Gross, I. Kaur, M. Ulirsch, and A. Werner, “Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization,” <i>arXiv:2312.12980</i>, 2023, doi: <a href="https://doi.org/10.1017/S2949764726100228">10.1017/S2949764726100228</a>. Gross, A., Kaur, I., Ulirsch, M., &#38; Werner, A. (2023). Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization. <i>ArXiv:2312.12980</i>. <a href="https://doi.org/10.1017/S2949764726100228">https://doi.org/10.1017/S2949764726100228</a> 663092026-07-08T06:24:15Z2026-07-08T08:29:27Z