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Cartier transform and
prismatic crystals
Michel Gros, Bernard Le Stum and Adolfo Quirós |
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Vol. 5 (2023), No. 3, 405–456
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Abstract |
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We show that the abstract equivalence of categories, called the Cartier transform, between crystals on the -crystalline and prismatic sites can be locally identified with the explicit local -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
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Mathematical Subject Classification
Primary: 05A30, 14F30, 14F40
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Milestones
Received: 18 March 2022
Revised: 6 March 2023
Accepted: 20 March 2023
Published: 2 November 2023
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Authors |
| Michel Gros | |
| Institut de Recherche Mathématique
(IRMAR) Université de Rennes I Rennes France |
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| Bernard Le Stum | |
| Institut de Recherche Mathématique
(IRMAR) Université de Rennes I Rennes France |
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| Adolfo Quirós | |
| Departamento de Matemáticas,
Facultad de Ciencias Universidad Autónoma de Madrid Campus de Cantoblanco Madrid Spain |
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| © 2023 MSP (Mathematical Sciences Publishers). |
