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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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Understanding absolute Galois group from its representations

Background. A major theme of modern number theory is to study the absolute Galois group $\text{Gal}(\overline{\mathbb Q} / \mathbb Q)$. Galois representation theory attempts to understand $\text{Gal}( …
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