# Perfectoid Spaces

@article{Scholze2012PerfectoidS,
title={Perfectoid Spaces},
author={P. Scholze},
journal={Publications math{\'e}matiques de l'IH{\'E}S},
year={2012},
volume={116},
pages={245-313}
}
• P. Scholze
• Published 2012
• Mathematics
• Publications mathématiques de l'IHÉS
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.
245 Citations
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