Perfectoid spaces and the homological conjectures - Yves André - ICM2018

Number Theory
Invited Lecture 3.11
Perfectoid spaces and the homological conjectures
Yves André
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.
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