The dimension theory of perfectoid spaces: an update.

Abstract: Chapter 11 of Atiyah-MacDonald proves a *dimension theory*—that is, it defines a few different notions of dimension, and proves that they are all the same. Later, Huber proved a dimension theory for adic spaces which are noetherian. We survey these results and discuss the analogous questions for perfectoid spaces. We will see that many things fail in the perfectoid situation, but maybe there is still some hope.

number theoryrepresentation theory

Audience: researchers in the topic

University of Utah Representation Theory / Number Theory Seminar