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

Şengün, Mehmet

doi:10.1090/S0002-9939-08-09435-5

The nonexistence of certain representations of the absolute Galois group of quadratic fields
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by Mehmet Haluk Şengün PDF

Proc. Amer. Math. Soc. 137 (2009), 27-35 Request permission

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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