Finding Galois splitting models to compute local invariants

Abstract

For prime $p$ and small $n$, Jones and Roberts have developed a database recording invariants for $p$-adic extensions of degree $n$. We contributed to this database by computing the Galois slope content, Galois mean slope, and inertia subgroup for a variety of wildly ramified extensions of composite degree using the idea of Galois splitting models. We will describe a number of strategies to find Galois splitting models including an original technique using generic polynomials and Panayi's root finding algorithm.