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
Abstract

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.

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