English

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.

Keywords

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

R2 v1 2026-06-23T00:03:38.176Z