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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Author: Mehmet Haluk Sengün
Journal: Proc. Amer. Math. Soc. 137 (2009), 27-35
MSC (2000): Primary 11F80, 11R39; Secondary 11G05
Published electronically: July 9, 2008
MathSciNet review: 2439421
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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.


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Additional Information

Mehmet Haluk Sengün
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

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09435-5
PII: S 0002-9939(08)09435-5
Keywords: Galois representations, quadratic number fields, elliptic curves
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
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.