  Let $p$ be a prime number. In this article we present a theorem, suggested by
Peter Scholze, which states that the absolute Galois group of $\mathbf{Q}_p$ is
the \'etale fundamental group of a certain object $Z$ which is defined over an
algebraically closed field. Thus, local Galois representations correspond to
local systems on $Z$. In brief, $Z$ is a (non-representable) quotient of a
perfectoid space. The construction combines two themes: the fundamental curve
of $p$-adic Hodge theory (due to Fargues-Fontaine) and the tilting equivalence
(due to Scholze).
