Twisted differential operators of negative level and prismatic crystals

Michel Gros (1) , Bernard Le Stum (1) , Adolfo Quirós (2)

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 UAM - Universidad Autónoma de Madrid

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 quasi-nilpotent twisted connection of level minus one and those of level zero. We explain how this is related to the existence of a Cartier operator on prismatic crystals. For the sake of readability, we limit ourselves to the case of dimension one.

Domaines: Géométrie algébrique [math.AG]

Michel Gros, Bernard Le Stum, Adolfo Quirós. Twisted differential operators of negative level and prismatic crystals. Tunisian Journal of Mathematics, 2022, 4, pp.19-53. ⟨10.2140/tunis.2022.4.19⟩. ⟨hal-02968767⟩