2002/11/14 by Lucia Di Vizio, Di Vizio, Lucia
Mathematics · #12H10 #12H25 #39A13 #65Q05 #FOS: Mathematics #Number Theory (math.NT) #Quantum Algebra (math.QA) #math.NT #math.QA #msc:12H10 #msc:12H25 #msc:39A13 #msc:65Q05
paper · pdf · doi:10.48550/arxiv.math/0211217
59 pages. Refereed version: some inaccuracies have been corrected. To appear in Geometric Aspects of Dwork's Theory (Dwork Trimester proceedings)
arxiv created 2003/05/22 · arxiv updated 2009/11/30
Inspired 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.