Perfectoid Spaces

@article{Scholze2012PerfectoidS,
  title={Perfectoid Spaces},
  author={Peter Scholze},
  journal={Publications math{\'e}matiques de l'IH{\'E}S},
  year={2012},
  volume={116},
  pages={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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