Cartier transform and prismatic crystals
arXiv:2203.09897 · doi:10.2140/tunis.2023.5.405
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.