Mathematics – Number Theory
Scientific paper
2010-09-30
Mathematics
Number Theory
12 pages
Scientific paper
In this paper, we consider mod $\ell$ Galois representations of $\mathbb{Q}$.
In particular, we obtain an effective criterion to distinguish two semisimple
2-dimensional, odd mod $\ell$ Galois representations up to isomorphism. Serre's
conjecture (Khare-Wintenberger's theorem), Sturm's theorem, and its
modification by Kohnen are used in our proof.
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