An introduction to perfectoid spaces and the tilting correspondence.
By Matthew Morrow
Direct summand conjecture and perfectoid Abhyankar lemma: an overview
By Yves André
Appears in collection : Arithmetic and Algebraic Geometry: A conference in honor of Ofer Gabber on the occasion of his 60th birthday
I will present a generalization of Scholze's perfectoid spaces that includes the limits of certain very ramified towers of log-regular rings. This is part of an on-going joint work with Ofer Gabber.