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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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