Vol. 304, No. 2, 2020

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Twisted calculus on affinoid algebras

Bernard Le Stum and Adolfo Quirós

Vol. 304 (2020), No. 2, 523–560

We introduce the notion of a twisted differential operator of given radius relative to an endomorphism σ of an affinoid algebra A. We show that this notion is essentially independent of the choice of the endomorphism σ. As a particular case, we obtain an explicit equivalence between modules endowed with a usual integrable connection (i.e., differential systems) and modules endowed with a σ-connection of the same radius (this concept generalizes both finite difference and q-difference systems). Moreover, this equivalence preserves cohomology and in particular solutions.

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arithmetic difference equations, twisted differential operators, twisted affinoid algebras, deformation, confluence, radius of convergence
Mathematical Subject Classification 2010
Primary: 12H10, 12H25, 14G22
Received: 15 December 2017
Revised: 24 July 2019
Accepted: 2 October 2019
Published: 12 February 2020
Bernard Le Stum
Institut de Recherche Mathematique (IRMAR)
Universite de Rennes I
Campus de Beaulieu
Adolfo Quirós
Departamento de Matemáticas
Universidad Autónoma de Madrid
Campus de Cantoblanco