## Closed subgroups of $GL_n(\widehat{\mathbb{Z}})$

This is a report of joint work with Chris Wallace. Coherent closed subgroups of $GL_n(\widehat{\mathbb{Z}})$ are, more or less, the $\widehat{\mathbb{Z}}$-valued points of an algebraic subgroup $G$ of $GL_n$ defined over the integers. This statement is relevant for the connection between motives and Galois theory.