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Cartier transform and prismatic crystals

Michel Gros, Bernard Le Stum and Adolfo Quirós

Vol. 5 (2023), No. 3, 405–456
Abstract

We show that the abstract equivalence of categories, called the Cartier transform, between crystals on the q-crystalline and prismatic sites can be locally identified with the explicit local q-twisted Simpson correspondence. This establishes four equivalences that are all compatible with the relevant cohomology theories. We restrict ourselves for simplicity to the one-dimensional case.

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Keywords
prism, crystal, differential operator
Mathematical Subject Classification
Primary: 05A30, 14F30, 14F40
Milestones
Received: 18 March 2022
Revised: 6 March 2023
Accepted: 20 March 2023
Published: 2 November 2023
Authors
Michel Gros
Institut de Recherche Mathématique (IRMAR)
Université de Rennes I
Rennes
France
Bernard Le Stum
Institut de Recherche Mathématique (IRMAR)
Université de Rennes I
Rennes
France
Adolfo Quirós
Departamento de Matemáticas, Facultad de Ciencias
Universidad Autónoma de Madrid
Campus de Cantoblanco
Madrid
Spain