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arXiv · 1907.10525

Prismatic Dieudonn\'e theory

Johannes Anschütz·Arthur-César Le Bras
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Abstract

We define, for each quasi-syntomic ring $R$ (in the sense of Bhatt-Morrow-Scholze), a category $\mathrm{DM}^{\rm adm}(R)$ of \textit{admissible prismatic Dieudonn\'e crystals over $R$} and a natural functor from $p$-divisible groups over $R$ to $\mathrm{DM}^{\rm adm}(R)$. 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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BibTeXRIS

Johannes Anschütz, Arthur-César Le Bras. 2019-07-24. Prismatic Dieudonn\'e theory. https://arxiv.org/abs/1907.10525

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