Nonsolvable number fields ramified only at 3 and 5

  title={Nonsolvable number fields ramified only at 3 and 5},
  author={Lassina Demb{\'e}l{\'e} and Matthew Greenberg and John Voight},
  journal={Compositio Mathematica},
  pages={716 - 734}
Abstract For p=3 and p=5, we exhibit a finite nonsolvable extension of ℚ which is ramified only at p, proving in the affirmative a conjecture of Gross. Our construction involves explicit computations with Hilbert modular forms. 


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Mazur's Principle for Totally Real Fields of Odd Degree

  • F. Jarvis
  • Mathematics
    Compositio Mathematica
  • 1999
In this paper, we prove an analogue of the result known as Mazur's Principle concerning optimal levels of mod ℓ Galois representations. The paper is divided into two parts. We begin with the study