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arXiv · 1801.10006

Perfectoid spaces and the homological conjectures

Yves Andre
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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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Yves Andre. 2018-01-30. Perfectoid spaces and the homological conjectures. https://arxiv.org/abs/1801.10006

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