9 citations · 14 across the 7 of their papers we have counts for
8 papers
Twisted differential operators of negative level and prismatic crystals
Michel Gros, Bernard Le Stum, Adolfo Quirós
We introduce twisted differential calculus of negative level and prove a descent theorem: Frobenius pullback provides an equivalence between finitely presented modules endowed with…
Twisted differential operators and -crystals
Michel Gros, Bernard Le Stum, Adolfo Quirós
We discuss the notion of a q-PD-envelope considered by Bhatt and Scholze in their recent theory of q-crystalline cohomology and explain the relation with our notion of a divided po…
Twisted calculus on affinoid algebras
Bernard Le Stum, Adolfo Quirós
We introduce the notion of a twisted differential operator of given radius relative to an endomorphism of an affinoid algebra A. We show that this notion is essentially indep…
Twisted divided powers and applications
Michel Gros, Bernard Le Stum, Adolfo Quirós
In order to give a formal treatment of differential equations in positive characteristic p, it is necessary to use divided powers. One runs into an analog problem in the theory of…
Formal confluence of quantum differential operators
Bernard Le Stum, Adolfo Quirós
We prove that a usual differential operator is formally the limit of quantum differential operators. For this purpose, we introduce the notion of twisted differential operator of i…
Twisted calculus
Bernard Le Stum, Adolfo Quirós
A twisted ring is a ring endowed with a family of endomorphisms satisfying certain relations. One may then consider the notions of twisted module and twisted differential module. W…
On quantum state of numbers
Bernard Le Stum, Adolfo Quirós
We introduce the notions of quantum characteristic and quantum flatness for arbitrary rings. More generally, we develop the theory of quantum integers in a ring and show that the h…
A Simpson correspondence in positive characteristic
Michel Gros, Bernard Le Stum, Adolfo Quirós
We define the -curvature map on the sheaf of differential operators of level on a scheme of positive characteristic as dual to some divided power map on infinitesimal…