English

Twisted calculus on affinoid algebras

Algebraic Geometry 2020-02-12 v1

Abstract

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

Keywords

Cite

@article{arxiv.1712.03745,
  title  = {Twisted calculus on affinoid algebras},
  author = {Bernard Le Stum and Adolfo Quirós},
  journal= {arXiv preprint arXiv:1712.03745},
  year   = {2020}
}
R2 v1 2026-06-22T23:14:06.407Z