An effective isomorphy criterion for mod $\ell$ Galois representations

Mathematics – Number Theory

Scientific paper

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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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