Perfectoid spaces

Abstract

The purpose of this course is to give an introduction to the theory of perfectoid spaces. We first give a summary of some basic constructions in perfectoid geometry. Second, we aim to give an idea of how perfectoid spaces arise “in nature” and how they are used: We discuss the pro-étale site and applications to $p$-adic Hodge theory, namely the construction of the Hodge–Tate spectral sequence. Our focus lies on discussing motivation, examples and the big picture, and less on completeness or technical details. But we at least give key ideas for all main proofs.