• Corpus ID: 198229510

Prismatic Dieudonn\'e theory

@article{Anschutz2019PrismaticDT,
  title={Prismatic Dieudonn\'e theory},
  author={Johannes Anschutz and Arthur-C'esar Le Bras},
  journal={arXiv: Algebraic Geometry},
  year={2019}
}
We define, for each quasi-syntomic ring $R$ (in the sense of Bhatt-Morrow-Scholze), a category $\mathrm{DF}(R)$ of \textit{filtered prismatic Dieudonn\'e crystals over $R$} and a natural functor from $p$-divisible groups over $R$ to $\mathrm{DF}(R)$. We prove that this functor is an antiequivalence. Our main cohomological tool is the prismatic formalism recently developed by Bhatt and Scholze. 
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