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Meghan De Witt

Publications and source records attributed to Meghan De Witt.

2 recordsLinked to original sources
arXiv2014

Finding Galois representations corresponding to certain Hecke eigenclasses

In 1992, Avner Ash and Mark McConnell presented computational evidence of a connection between three-dimensional Galois representations and certain arithmetic cohomology classes. For some examples they were unable to determine the attached representation. For several Hecke eigenclasses (including one for which Ash and McConnell did not find the Galois representation), we find a Galois representation which appears to be attached and show strong evidence for the uniqueness of this representation. The techniques that we use to find defining polynomials for the Galois representations include a targeted Hunter search, class field theory, and elliptic curves.

math.NT↗
arXiv2014

Minimal ramification and the inverse Galois problem over the rational function field $\mathbb{F}_p(t)$

The inverse Galois problem is concerned with finding a Galois extension of a field $K$ with given Galois group. In this paper we consider the particular case where the base field is $K=\F_p(t)$. We give a conjectural formula for the minimal number of primes, both finite and infinite, ramified in $G$-extensions of $K$, and give theoretical and computational proofs for many cases of this conjecture.

math.NT↗