Higher Algebra

The course consists in an introduction to non-archimedean arithmetic geometry using the language of adic spaces, formal schemes and condensed rings. We will provide some fundamental examples such as Tate's analytic varieties, Scholze's perfectoid spaces and the Fargues-Fontaine curve. We will discuss applications of this formalism to the study of p-adic cohomology theories.

By the end of the course, students will be able to handle the language and techniques of modern non-archimedean geometry, which are the foundations of the recent developments in p-adic Hodge theory.