Prismatic $F$-crystals and crystalline Galois representations

Bhargav Bhatt; Peter Scholze

Prismatic $F$-crystals and crystalline Galois representations

Number Theory 2023-09-13 v2 Algebraic Geometry

Authors: Bhargav Bhatt , Peter Scholze

Abstract

Let $K$ be a complete discretely valued field of mixed characteristic $(0,p)$ with perfect residue field. We prove that the category of prismatic $F$ -crystals on $\mathcal O_K$ is equivalent to the category of lattices in crystalline $G_K$ -representations.

Keywords

prismatic f-crystals crystalline galois representations discretely valued field mixed characteristic lattices

Cite

@article{arxiv.2106.14735,
  title  = {Prismatic $F$-crystals and crystalline Galois representations},
  author = {Bhargav Bhatt and Peter Scholze},
  journal= {arXiv preprint arXiv:2106.14735},
  year   = {2023}
}

Comments

v2: small updates

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