@unpublished{58852,
  abstract     = {{We study the asymptotic distribution of wildly ramified extensions of
function fields in characteristic $p > 2$, focusing on (certain) $p$-groups of
nilpotency class at most $2$. Rather than the discriminant, we count extensions
according to an invariant describing the last jump in the ramification
filtration at each place. We prove a local-global principle relating the
distribution of extensions over global function fields to their distribution
over local fields, leading to an asymptotic formula for the number of
extensions with a given global last-jump invariant. A key ingredient is
Abrashkin's nilpotent Artin-Schreier theory, which lets us parametrize
extensions and obtain bounds on the ramification of local extensions by
estimating the number of solutions to certain polynomial equations over finite
fields.}},
  author       = {{Gundlach, Fabian and Seguin, Beranger Fabrice}},
  booktitle    = {{arXiv:2502.18207}},
  title        = {{{Counting two-step nilpotent wildly ramified extensions of function  fields}}},
  year         = {{2025}},
}