Questions relating to the representations of the absolute Galois group $\mathrm{Gal}(\overline K/K)$ of a number field or of a local field.

Many objects that arise in number theory are naturally Galois representations. For example, if $L$ is a Galois extension of a number field $K$, the ring of integers $O_L$ of $L$ is a Galois module over $O_K$ for the Galois group of $L/K$ (see Hilbert–Speiser theorem). If $K$ is a local field, the multiplicative group of its separable closure is a module for the absolute Galois group of $K$ and its study leads to local class field theory. For global class field theory, the union of the idele class groups of all finite separable extensions of $K$ is used instead (Wikipedia).