{"author":[{"first_name":"Fabian","last_name":"Gundlach","id":"100450","full_name":"Gundlach, Fabian"},{"first_name":"Beranger Fabrice","last_name":"Seguin","orcid":"0000-0002-4800-4647","full_name":"Seguin, Beranger Fabrice","id":"102487"}],"date_created":"2026-03-17T12:17:42Z","date_updated":"2026-03-17T12:21:09Z","title":"Lifts of unramified twists and local-global principles","citation":{"ieee":"F. Gundlach and B. F. Seguin, “Lifts of unramified twists and local-global principles,” <i>arXiv:2603.15544</i>. 2026.","chicago":"Gundlach, Fabian, and Beranger Fabrice Seguin. “Lifts of Unramified Twists and Local-Global Principles.” <i>ArXiv:2603.15544</i>, 2026.","ama":"Gundlach F, Seguin BF. Lifts of unramified twists and local-global principles. <i>arXiv:260315544</i>. Published online 2026.","apa":"Gundlach, F., &#38; Seguin, B. F. (2026). Lifts of unramified twists and local-global principles. In <i>arXiv:2603.15544</i>.","short":"F. Gundlach, B.F. Seguin, ArXiv:2603.15544 (2026).","bibtex":"@article{Gundlach_Seguin_2026, title={Lifts of unramified twists and local-global principles}, journal={arXiv:2603.15544}, author={Gundlach, Fabian and Seguin, Beranger Fabrice}, year={2026} }","mla":"Gundlach, Fabian, and Beranger Fabrice Seguin. “Lifts of Unramified Twists and Local-Global Principles.” <i>ArXiv:2603.15544</i>, 2026."},"year":"2026","user_id":"100450","_id":"65031","external_id":{"arxiv":["2603.15544"]},"language":[{"iso":"eng"}],"publication":"arXiv:2603.15544","type":"preprint","status":"public","abstract":[{"lang":"eng","text":"We prove that two-step nilpotent $p$-extensions of rational global function fields of characteristic $p$ satisfy a quantitative local-global principle when they are counted according to their largest upper ramification break (\"last jump\"). We had previously shown this only for $p\\neq2$. Compared to our previous proof, this proof is also more self-contained, and may apply to heights other than the last jump. As an application, we describe the distribution of last jumps of $D_4$-extensions of rational global function fields of characteristic $2$. We also exhibit a counterexample to the analogous local-global principle when counting by discriminants."}]}