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.