Perfectoid spaces and the homological conjectures
Commutative Algebra
2018-01-31 v1
Abstract
This is a survey of recent advances in commutative algebra, especially in mixed characteristic, obtained by using the theory of perfectoid spaces. An explanation of these techniques and a short account of the author's proof of the direct summand conjecture are included. One then portrays the progresses made with these (and related) techniques on the so-called homological conjectures.
Cite
@article{arxiv.1801.10006,
title = {Perfectoid spaces and the homological conjectures},
author = {Yves Andre},
journal= {arXiv preprint arXiv:1801.10006},
year = {2018}
}
Comments
intended for the ICM 2018