Publications mathématiques de l'IHÉS

, Volume 116, Issue 1, pp 245–313 | Cite as

Perfectoid Spaces

  • Peter Scholze


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.


Topological Space Toric Variety Inverse Limit Absolute Galois Group Rational Subset 
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© IHES and Springer-Verlag 2012

Authors and Affiliations

  1. 1.Mathematisches InstitutUniversität BonnBonnGermany

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