On the existence of large degree Galois representations for fields of small discriminant

Abstract

Let $L/K$ be a Galois extension of number fields. We prove two lower bounds on the maximum of the degrees of the irreducible complex representations of $\mathrm{Gal}(L/K)$, the sharper of which is conditional on the Artin Conjecture and the Generalized Riemann Hypothesis. Our bound is nontrivial when $[K:\mathbb{Q}]$ is small and $L$ has small root discriminant, and might be summarized as saying that such fields can't be "too abelian."

arXiv commentUpdate on history of discriminant bounds in introduction

Cited by in corpus (1)

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