Publications mathématiques de l'IHÉS

, Volume 116, Issue 1, pp 245-313

First online:

Perfectoid Spaces

  • Peter ScholzeAffiliated withMathematisches Institut, Universität Bonn Email author 

Rent the article at a discount

Rent now

* Final gross prices may vary according to local VAT.

Get Access


We introduce a certain class of so-called perfectoid rings and spaces, which give a natural framework for Faltings’ almost purity theorem, and for which there is a natural tilting operation which exchanges characteristic 0 and characteristic p. We deduce the weight-monodromy conjecture in certain cases by reduction to equal characteristic.