Echelons of power series and Gabrielov's counterexample to nested linear Artin approximation
This work was done in part during a Research-in-Teams program at the Erwin-Schrödinger Institute at Vienna, and the special semester on Artin approximation within the Chaire Jean Morlet at CIRM, Luminy-Marseille. M.E.A. was supported by MINECO MTM2014-55565 and UCM , IMI and Grupo 910444, F.-J.C.-J. by MTM2013-40455-P, MTM2016-75024-P and FEDER, H.H. and C.K. by the Austrian Science Fund FWF, within the projects P-25652 and AI-0038211, respectively, P29467-N32 and F5011-N15.
Abstract
Gabrielov's famous example for the failure of analytic Artin approximation in the presence of nested subring conditions is shown to be due to a growth phenomenon in standard basis computations for echelons, a generalization of the concept of ideals in power series rings.
