Let $X$ be a 3-dimensional hyperbolic variety which is a quotient of hyperbolic 3-space by an “arithmetic” group of isometries. The Langlands program predicts that the singular cohomology of $X$ with coefficients in $\mathbf Z/n\mathbf Z$ should have a natural action of the absolute Galois group of a number field, even though $X$ is not an algebraic variety. The idea is to realize the torsion cohomology of $X$ as parts of the torsion cohomology of another locally symmetric space that happens to be a Shimura variety, hence an algebraic variety defined over a number field. This idea has been succesfully implemented by Harris-Lan-Taylor-Thorne, Scholze and Boxer (independently and in chronological order) ; their articles actually treat a much more general case, that of the locally symmetric spaces of a general linear group over a totally real or CM number field. We will try to explain Scholze's approach.