Proceedings of the Japan Academy, Series A, Mathematical Sciences

The non-existence of certain mod 2 Galois representations of some small quadratic fields

Hyunsuk Moon and Yuichiro Taguchi

Full-text: Open access

Abstract

For a few quadratic fields, the non-existence is proved of continuous irreducible mod 2 Galois representations of degree 2 unramified outside $\{2,\infty\}$.

Article information

Source
Proc. Japan Acad. Ser. A Math. Sci., Volume 84, Number 5 (2008), 63-67.

Dates
First available in Project Euclid: 1 May 2008

Permanent link to this document
https://projecteuclid.org/euclid.pja/1209649654

Digital Object Identifier
doi:10.3792/pjaa.84.63

Mathematical Reviews number (MathSciNet)
MR2415898

Zentralblatt MATH identifier
1165.11052

Subjects
Primary: 11R39: Langlands-Weil conjectures, nonabelian class field theory [See also 11Fxx, 22E55] 11F80: Galois representations 11R32: Galois theory

Keywords
Mod $p$ Galois representation non-existence Serre’s modularity conjecture

Citation

Moon, Hyunsuk; Taguchi, Yuichiro. The non-existence of certain mod 2 Galois representations of some small quadratic fields. Proc. Japan Acad. Ser. A Math. Sci. 84 (2008), no. 5, 63--67. doi:10.3792/pjaa.84.63. https://projecteuclid.org/euclid.pja/1209649654


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References

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