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The term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring, but can also be used as a synonym for G-module. The study of Galois modules for extensions of local or global fields is an important tool in number theory.

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Irreducibility of Tate module (as a Galois representation) of elliptic curves with good redu...

Let me upgrade my comment to an answer: There exist (simple) abelian varieties over $\mathbb{Q}_{p}$ of every dimension $g\geq 2$ with supersingular good reduction and non-semisimple Tate module. Abel …
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