[{"abstract":[{"lang":"eng","text":"<jats:title>Abstract</jats:title>\r\n                  <jats:p>\r\n                    Let\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2949764726100228_inline1.png\"/>\r\n                        <jats:tex-math>$A$</jats:tex-math>\r\n                      </jats:alternatives>\r\n                    </jats:inline-formula>\r\n                    be an abelian variety with totally degenerate reduction over a non-Archimedean field. We describe the moduli space of semi-homogeneous vector bundles on\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2949764726100228_inline2.png\"/>\r\n                        <jats:tex-math>$A$</jats:tex-math>\r\n                      </jats:alternatives>\r\n                    </jats:inline-formula>\r\n                    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\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2949764726100228_inline3.png\"/>\r\n                        <jats:tex-math>$H=0$</jats:tex-math>\r\n                      </jats:alternatives>\r\n                    </jats:inline-formula>\r\n                    our moduli space may be identified with the moduli space\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2949764726100228_inline4.png\"/>\r\n                        <jats:tex-math>$M_{0,r}(A)$</jats:tex-math>\r\n                      </jats:alternatives>\r\n                    </jats:inline-formula>\r\n                    of semi-stable vector bundles with vanishing Chern classes on\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2949764726100228_inline5.png\"/>\r\n                        <jats:tex-math>$A$</jats:tex-math>\r\n                      </jats:alternatives>\r\n                    </jats:inline-formula>\r\n                    . In this case we construct a surjective analytic morphism from the character variety of the analytic fundamental group of\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2949764726100228_inline6.png\"/>\r\n                        <jats:tex-math>$A$</jats:tex-math>\r\n                      </jats:alternatives>\r\n                    </jats:inline-formula>\r\n                    onto\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2949764726100228_inline7.png\"/>\r\n                        <jats:tex-math>$M_{0,r}(A)$</jats:tex-math>\r\n                      </jats:alternatives>\r\n                    </jats:inline-formula>\r\n                    , which naturally tropicalizes. One may view this construction as a non-Archimedean uniformization of\r\n                    <jats:inline-formula>\r\n                      <jats:alternatives>\r\n                        <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S2949764726100228_inline8.png\"/>\r\n                        <jats:tex-math>$M_{0,r}(A)$</jats:tex-math>\r\n                      </jats:alternatives>\r\n                    </jats:inline-formula>\r\n                    .\r\n                  </jats:p>"}],"citation":{"apa":"Gross, A., Kaur, I., Ulirsch, M., &#38; Werner, A. (2026). Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization. <i>Moduli</i>, <i>3</i>, Article e8. <a href=\"https://doi.org/10.1017/S2949764726100228\">https://doi.org/10.1017/S2949764726100228</a>","ieee":"A. Gross, I. Kaur, M. Ulirsch, and A. Werner, “Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization,” <i>Moduli</i>, vol. 3, Art. no. e8, 2026, doi: <a href=\"https://doi.org/10.1017/S2949764726100228\">10.1017/S2949764726100228</a>.","short":"A. Gross, I. Kaur, M. Ulirsch, A. Werner, Moduli 3 (2026).","chicago":"Gross, Andreas, Inder Kaur, Martin Ulirsch, and Annette Werner. “Semi-Homogeneous Vector Bundles on Abelian Varieties: Moduli Spaces and Their Tropicalization.” <i>Moduli</i> 3 (2026). <a href=\"https://doi.org/10.1017/S2949764726100228\">https://doi.org/10.1017/S2949764726100228</a>.","mla":"Gross, Andreas, et al. “Semi-Homogeneous Vector Bundles on Abelian Varieties: Moduli Spaces and Their Tropicalization.” <i>Moduli</i>, vol. 3, e8, Cambridge University Press (CUP), 2026, doi:<a href=\"https://doi.org/10.1017/S2949764726100228\">10.1017/S2949764726100228</a>.","ama":"Gross A, Kaur I, Ulirsch M, Werner A. Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization. <i>Moduli</i>. 2026;3. doi:<a href=\"https://doi.org/10.1017/S2949764726100228\">10.1017/S2949764726100228</a>","bibtex":"@article{Gross_Kaur_Ulirsch_Werner_2026, title={Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization}, volume={3}, DOI={<a href=\"https://doi.org/10.1017/S2949764726100228\">10.1017/S2949764726100228</a>}, number={e8}, journal={Moduli}, publisher={Cambridge University Press (CUP)}, author={Gross, Andreas and Kaur, Inder and Ulirsch, Martin and Werner, Annette}, year={2026} }"},"publication":"Moduli","type":"journal_article","date_created":"2026-07-08T06:24:15Z","intvolume":"         3","publication_status":"published","date_updated":"2026-07-09T07:05:30Z","publication_identifier":{"issn":["2949-7647","2977-1382"]},"author":[{"full_name":"Gross, Andreas","last_name":"Gross","first_name":"Andreas"},{"last_name":"Kaur","first_name":"Inder","full_name":"Kaur, Inder"},{"full_name":"Ulirsch, Martin","last_name":"Ulirsch","first_name":"Martin","id":"114697"},{"full_name":"Werner, Annette","last_name":"Werner","first_name":"Annette"}],"status":"public","year":"2026","title":"Semi-homogeneous vector bundles on abelian varieties: moduli spaces and their tropicalization","volume":3,"user_id":"82981","doi":"10.1017/S2949764726100228","_id":"66309","publisher":"Cambridge University Press (CUP)","language":[{"iso":"eng"}],"article_number":"e8"}]