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Twisted calculus on
affinoid algebras
Bernard Le Stum and Adolfo Quirós |
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Vol. 304 (2020), No. 2, 523–560
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Abstract |
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We introduce the notion of a twisted differential operator of given radius relative to an endomorphism of an affinoid algebra . We show that this notion is essentially independent of the choice of the endomorphism . 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 -connection of the same radius (this concept generalizes both finite difference and -difference systems). Moreover, this equivalence preserves cohomology and in particular solutions. |
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Keywords
arithmetic difference equations, twisted differential
operators, twisted affinoid algebras, deformation,
confluence, radius of convergence
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Mathematical Subject Classification 2010
Primary: 12H10, 12H25, 14G22
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Milestones
Received: 15 December 2017
Revised: 24 July 2019
Accepted: 2 October 2019
Published: 12 February 2020
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Authors |
| Bernard Le Stum | |
| Institut de Recherche Mathematique
(IRMAR) Universite de Rennes I Campus de Beaulieu Rennes France |
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| Adolfo Quirós | |
| Departamento de Matemáticas Universidad Autónoma de Madrid Campus de Cantoblanco Madrid Spain |
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