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arXiv · 1712.03745

Twisted calculus on affinoid algebras

Bernard Le Stum·Adolfo Quirós
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Abstract

We introduce the notion of a twisted differential operator of given radius relative to an endomorphism $$\sigma$$ of an affinoid algebra A. We show that this notion is essentially independent of the choice of the endomorphism $$\sigma$$. 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 $$\sigma$$-connection of the same radius (i.e. q-difference systems). Moreover, this equivalence preserves cohomology and in particular solutions.

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Bernard Le Stum, Adolfo Quirós. 2017-12-11. Twisted calculus on affinoid algebras. https://doi.org/10.2140/pjm.2020.304.523

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