## The nonexistence of certain representations of the absolute Galois group of quadratic fields

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- by Mehmet Haluk Şengün
- Proc. Amer. Math. Soc.
**137**(2009), 27-35 - DOI: https://doi.org/10.1090/S0002-9939-08-09435-5
- Published electronically: July 9, 2008
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## Abstract:

For a quadratic field $K$, we investigate continuous mod $p$ representations of $Gal(\overline {K}/K)$ that are unramified away from $\{p,\infty \}$. We prove that for certain $(K,p)$ there are no such irreducible representations. We also list some imaginary quadratic fields for which such irreducible representations exist. As an application, we look at elliptic curves with good reduction away from $2$ over quadratic fields.## References

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## Bibliographic Information

**Mehmet Haluk Şengün**- Affiliation: Department of Mathematics, University of Wisconsin, 480 Lincoln Drive, Madison, Wisconsin 53706
- Address at time of publication: Department of Mathematics, University of Duisburg-Essen, Universitäts- strasse 2, 45117 Essen, Germany
- Email: sengun@math.wisc.edu
- Received by editor(s): September 18, 2007
- Received by editor(s) in revised form: November 25, 2007
- Published electronically: July 9, 2008
- Communicated by: Ken Ono
- © Copyright 2008
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**137**(2009), 27-35 - MSC (2000): Primary 11F80, 11R39; Secondary 11G05
- DOI: https://doi.org/10.1090/S0002-9939-08-09435-5
- MathSciNet review: 2439421