Vol. 4, No. 1, 2022

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Twisted differential operators of negative level and prismatic crystals

Michel Gros, Bernard Le Stum and Adolfo Quirós

Vol. 4 (2022), No. 1, 19–54
DOI: 10.2140/tunis.2022.4.19

We introduce twisted differential calculus of negative level and prove a descent theorem: Frobenius pullback provides an equivalence between finitely presented modules endowed with a topologically quasinilpotent twisted connection of level minus one and those of level zero. We explain how this is related to the existence of a Cartier transform on prismatic crystals. For the sake of readability, we limit ourselves to the case of dimension one.

prism, crystal, differential operator
Mathematical Subject Classification
Primary: 05A30, 13N10, 14F30, 14F40
Received: 9 October 2020
Revised: 23 March 2021
Accepted: 22 April 2021
Published: 30 March 2022
Michel Gros
Université de Rennes 1
Campus de Beaulieu
35042 Rennes Cedex
Bernard Le Stum
Institut de Recherche Mathematique (IRMAR)
Universite de Rennes I
263 Avenue du General Leclerc
CS 74205
35042 Rennes CEDEX
Adolfo Quirós
Departamento de Matemáticas
Universidad Autónoma de Madrid
Campus de Cantoblanco
28049 Madrid