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. 
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    References

    SHOWING 1-10 OF 39 REFERENCES
    Galois representations arising from some compact Shimura varieties
    • 150
    • PDF
    Almost ring theory
    • 152
    • Highly Influential
    • PDF
    Monodromy weight filtration is independent of l
    • 10
    • PDF
    On arithmetic families of filtered -modules and crystalline representations
    • 10
    • PDF
    Weight-monodromy conjecture for p-adically uniformized varieties
    • 56
    • PDF
    Étale Cohomology of Rigid Analytic Varieties and Adic Spaces
    • 266
    • Highly Influential
    Spectral Theory and Analytic Geometry over Non-Archimedean Fields
    • 758
    • PDF
    Théorie de Lubin-Tate non-abélienne et représentations elliptiques
    • 35
    • PDF
    Prime ideal structure in commutative rings
    • 538
    • PDF
    Compatibility of Local and Global Langlands Correspondences
    • 132
    • PDF