Twisted differential operators and q-crystals

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

1 IRMAR - Institut de Recherche Mathématique de Rennes
2 Departamento de Matemáticas

We describe explicitly the q-PD-envelopes considered by Bhatt and Scholze in their recent theory of q-crystalline cohomology and explain the relation with our notion of a divided polynomial twisted algebra. Together with an interpretation of crystals on the q-crystalline site, that we call q-crystals, as modules endowed with some kind of stratification, it allows us to associate a module on the ring of twisted differential operators to any q-crystal.

Domaines: Géométrie algébrique [math.AG]

Michel Gros, Bernard Le Stum, Adolfo Quirós. Twisted differential operators and q-crystals. 2020. ⟨hal-02559467⟩