On the existence of large degree Galois representations for fields of small discriminant
Rouse, Jeremy · Thorne, Frank
Original · EN
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 Gal(L/K), the sharper of which is conditional on the Artin Conjecture and the Generalized Riemann Hypothesis. Our bound is nontrivial when [K: Q] is small and L has small root discriminant, and might be summarized as saying that such fields can't be "too abelian."
English translation
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