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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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Evidence for the equivariant BSD conjecture with higher multiplicity

Let $E/\mathbb{Q}$ be an elliptic curve and let $\rho$ be an irreducible Artin representation. Let $K_\rho/\mathbb{Q}$ be the smallest Galois extension such that $\rho$ factors through $\mathrm{Gal}(K …
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