Prismatic Dieudonn\'e theory
Algebraic Geometry
2022-10-12 v4 Number Theory
Abstract
We define, for each quasi-syntomic ring (in the sense of Bhatt-Morrow-Scholze), a category of \textit{admissible prismatic Dieudonn\'e crystals over } and a natural functor from -divisible groups over to . 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