2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/65649Inspired by the theory of p-adic differential equations, this paper introduces an analogous theory for q-difference equations over a local field, when |q|=1. We define some basic concepts, for instance the generic radius of convergence, introduce technical tools, such as a twisted Taylor formula for analytic functions, and prove some fundamental statements, such as an effective bound theorem, the existence of a weak Frobenius structure and a transfer theorem in regular singular disks.59 pages. Refereed version: some inaccuracies have been corrected. To appear in Geometric Aspects of Dwork's Theory (Dwork Trimester proceedings)Number TheoryQuantum Algebra12H10, 12H25, 39A13, 65Q05text