Prismatic $F$-crystals and crystalline Galois representations

Bhargav Bhatt; Peter Scholze

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arXiv · 2106.14735

Prismatic $F$-crystals and crystalline Galois representations

Bhargav Bhatt·Peter Scholze

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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.

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Bhargav Bhatt, Peter Scholze. 2021-06-28. Prismatic $F$-crystals and crystalline Galois representations. https://arxiv.org/abs/2106.14735

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