# Nonsolvable number fields ramified only at 3 and 5

@article{Dembl2009NonsolvableNF,
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},
year={2009},
volume={147},
pages={716 - 734}
}
• Published 24 June 2009
• Mathematics
• Compositio Mathematica
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## References

SHOWING 1-10 OF 63 REFERENCES

We prove that there is no primitive octic number field ramified only at one small prime, and so no such number field with a nonsolvable Galois group.
We find all number fields which can be generated from a degree 7 polynomial satisfying the conditions that only one prime, p, ramifies and p< 11.
Abstract Let ρ be a two-dimensional semisimple odd representation of Gal ( Q / Q ) over a finite field of characteristic 5 which is unramified outside 5. Assuming the GRH, we show in accordance with
Serre's conjecture predicts the nonexistence of certain nonsolvable Galois extensions of ℚ which are unramified outside one small prime. These nonexistence theorems have been proven by the techniques
It is shown that there are exactly 858 Shimura curves X D 0 (R) of genus at most two, up to equivalence, which are related to each other by the inequality of the following type.
Ideas and techniques from Khare´s and Wintenberger’s preprint on the proof of Serre’s conjecture for odd conductors are used to establish that for a fixed prime l infinitely many of the groups
This article presents an algorithm to compute Hilbert modular forms on the quadratic field ℚ(√5) with prime level of norm less than 100 (up toℚ-isogeny).
In this paper we show that an odd Galois representation ?P?I : Gal( ?PQ/Q) ?? GL2(F9) having nonsolvable image and satisfying certain local conditions at 3 and 5 is modular. Our main tools are ideas
• 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