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Nonsolvable number fields ramified only at 3 and 5

  • Lassina Dembélé (a1), Matthew Greenberg (a2) and John Voight (a3)
Abstract
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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[8] G. Cardona and J. Quer , Field of moduli and field of definition for curves of genus 2, in Computational aspects of algebraic curves, Lecture Notes Series on Computing, vol. 13 (World Scientific, Hackensack, NJ, 2005), 7183.

[40] J.-P. Serre , Congruences et formes modulaires [d’après H. P. F. Swinnerton-Dyer], in Séminaire Bourbaki, 24e année (1971/1972), exp. no. 416, Lecture Notes in Mathematics, vol. 317 (Springer, Berlin, 1973), 319338.

[53] G. Wiese , On projective linear groups over finite fields as Galois groups over the rational numbers, in Modular forms on Schiermonnikoog, eds Bas Edixhoven , Gerard van der Geer and Ben Moonen (Cambridge University Press, Cambridge, 2008), 343350.

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Compositio Mathematica
  • ISSN: 0010-437X
  • EISSN: 1570-5846
  • URL: /core/journals/compositio-mathematica
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