Kevin Keating

activity

20242026

collaborators

5 papers

math.NT2026

Distinguished defining polynomials for extensions of p-adic fields

Jordi Guàrdia i Rúbies, John W. Jones, Kevin Keating +3

We give an algorithm for choosing a distinguished defining polynomial for a p-adic field extension. This algorithm formed an important ingredient in the recent expansion of the dat…

math.NT2025

Some nonabelian subgroups of the Nottingham group over F_4

Kevin Keating

We classify the conjugacy classes of minimally ramified nonabelian subgroups of order 8 in the Nottingham group $N (F_{4})$ . We then use finite automata to give explicit descriptions…

math.NT2025

Families of p-adic fields

Jordi Guàrdia Rúbies, John W. Jones, Kevin Keating +3

We improve the database of $p$ -adic fields in the LMFDB by systematically using Krasner-Monge polynomials and working relatively as well as absolutely. These improvements organize…

math.NT2025

Artin-Schreier-Witt extensions and ramification breaks

G. Griffith Elder, Kevin Keating

Let $K = k ((t))$ be a local field of characteristic $p > 0$ , with perfect residue field $k$ . Let $a = (a_{0}, a_{1}, \dots, a_{n - 1}) \in W_{n} (K)$ be a Witt vector of length $n$ . Artin-Schre…

math.NT2024

Galois scaffolds for extraspecial p-extensions in characteristic 0

Kevin Keating, Paul Schwartz

Let $K$ be a local field of characteristic 0 with residue characteristic $p$ . Let $G$ be an extraspecial $p$ -group and let $L / K$ be a totally ramified $G$ -extension. In this paper…