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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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