{"language":[{"iso":"eng"}],"date_created":"2025-02-26T08:51:57Z","author":[{"last_name":"Gundlach","first_name":"Fabian","full_name":"Gundlach, Fabian","id":"100450"},{"full_name":"Seguin, Beranger Fabrice","id":"102487","first_name":"Beranger Fabrice","last_name":"Seguin"}],"date_updated":"2025-02-26T08:53:08Z","external_id":{"arxiv":["2502.18207"]},"status":"public","publication":"arXiv:2502.18207","citation":{"apa":"Gundlach, F., &#38; Seguin, B. F. (2025). Counting two-step nilpotent wildly ramified extensions of function  fields. In <i>arXiv:2502.18207</i>.","ama":"Gundlach F, Seguin BF. Counting two-step nilpotent wildly ramified extensions of function  fields. <i>arXiv:250218207</i>. Published online 2025.","short":"F. Gundlach, B.F. Seguin, ArXiv:2502.18207 (2025).","ieee":"F. Gundlach and B. F. Seguin, “Counting two-step nilpotent wildly ramified extensions of function  fields,” <i>arXiv:2502.18207</i>. 2025.","mla":"Gundlach, Fabian, and Beranger Fabrice Seguin. “Counting Two-Step Nilpotent Wildly Ramified Extensions of Function  Fields.” <i>ArXiv:2502.18207</i>, 2025.","bibtex":"@article{Gundlach_Seguin_2025, title={Counting two-step nilpotent wildly ramified extensions of function  fields}, journal={arXiv:2502.18207}, author={Gundlach, Fabian and Seguin, Beranger Fabrice}, year={2025} }","chicago":"Gundlach, Fabian, and Beranger Fabrice Seguin. “Counting Two-Step Nilpotent Wildly Ramified Extensions of Function  Fields.” <i>ArXiv:2502.18207</i>, 2025."},"year":"2025","user_id":"100450","type":"preprint","_id":"58852","abstract":[{"text":"We study the asymptotic distribution of wildly ramified extensions of\r\nfunction fields in characteristic $p > 2$, focusing on (certain) $p$-groups of\r\nnilpotency class at most $2$. Rather than the discriminant, we count extensions\r\naccording to an invariant describing the last jump in the ramification\r\nfiltration at each place. We prove a local-global principle relating the\r\ndistribution of extensions over global function fields to their distribution\r\nover local fields, leading to an asymptotic formula for the number of\r\nextensions with a given global last-jump invariant. A key ingredient is\r\nAbrashkin's nilpotent Artin-Schreier theory, which lets us parametrize\r\nextensions and obtain bounds on the ramification of local extensions by\r\nestimating the number of solutions to certain polynomial equations over finite\r\nfields.","lang":"eng"}],"title":"Counting two-step nilpotent wildly ramified extensions of function  fields"}