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Journal Articles Tunisian Journal of Mathematics Year : 2022

Cartier transform and prismatic crystals

Abstract

We show that the abstract equivalence of categories, called 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 dimension one situation.

Dates and versions

hal-03943285 , version 1 (20-10-2022)
hal-03943285 , version 2 (17-01-2023)

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Cite

Michel Gros, Bernard Le Stum, Adolfo Quirós. Cartier transform and prismatic crystals. Tunisian Journal of Mathematics, 2022, 5 (3), pp.405-456. ⟨10.2140/tunis.2023.5.405⟩. ⟨hal-03943285v2⟩
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