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

Author(s): Mehmet Haluk Sengün
Journal: Proc. Amer. Math. Soc. 137 (2009), 27-35.
MSC (2000): Primary 11F80, 11R39; Secondary 11G05
Posted: 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.

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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, Universitätsstrasse 2, 45117 Essen, Germany
Email: sengun@math.wisc.edu

DOI: 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
Posted: July 9, 2008
Communicated by: Ken Ono
Copyright of article: Copyright 2008, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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