English

Prismatic Dieudonn\'e theory

Algebraic Geometry 2022-10-12 v4 Number Theory

Abstract

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

Keywords

Cite

@article{arxiv.1907.10525,
  title  = {Prismatic Dieudonn\'e theory},
  author = {Johannes Anschütz and Arthur-César Le Bras},
  journal= {arXiv preprint arXiv:1907.10525},
  year   = {2022}
}

Comments

Replaced the notion of filtered prismatic Dieudonn\'e crystal by the equivalent (but simpler) notion of admissible prismatic Dieudonn\'e crystal; corrected and simplified (following a suggestion of Mathew) the proof of fully faithfulness; many small changes

R2 v1 2026-06-23T10:29:35.415Z