Remarks on Artin approximation with constraints

2017/07/26 by Popescu, Dorin, Rond, Guillaume
#Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.1707.08346

Abstract

We study various approximation results of solutions of equations f(x,Y)=0 where f(x,Y)∈\mathbb K[[x]][Y]^r and x and Y are two sets of variables, and where some components of the solutions y(x)∈\mathbb K[[x]]^m do not depend on all the variables x_j. These problems have been highlighted by M. Artin.

Related

• Formal and convergent solutions of analytic equations
• Bornes effectives des fonctions d'approximation des solutions formelles d'équations binomiales
• Diophantine approximation with constraints
• Nested Artin Strong Approximation Property
• Lojasiewicz inequality over the ring of power series in two variables