Perfectoid Spaces

Scholze, Peter

Publications Mathématiques de l'IHÉS, Tome 116 (2012), pp. 245-313.

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.

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