A perfectoid space is a type of analytic space in non-Archimedean geometry introduced by Scholze (2012). It is locally obtained from a perfectoid algebra over a perfectoid field in the sense of adic geometry.
The tilting construction associates to a perfectoid space in mixed characteristic a perfectoid space in characteristic 
while preserving its underlying topological space and its
finite étale covers. This provides a bridge between arithmetic
geometry in the two characteristics.
