7 citations · 15 across the 15 of their papers we have counts for
13 papers · 1 filter
Artin approximation over Banach spaces
Guillaume Rond
We give examples showing that the usual Artin Approximation theorems valid for convergent series over a field are no longer true for convergent series over a commutative Banach alg…
Finiteness results concerning algebraic power series
Fuensanta Aroca, Julie Decaup, Guillaume Rond
We construct an explicit filtration of the ring of algebraic power series by finite dimensional constructible sets, measuring the complexity of these series. As an application, we…
The minimal cone of an algebraic Laurent series
Fuensanta Aroca, Julie Decaup, Guillaume Rond
We study the algebraic closure of , the field of power series in several indeterminates over a field . In characteristic zero we show that the elemen…
Support of Laurent series algebraic over the field of formal power series
Fuensanta Aroca, Guillaume Rond
This work is devoted to the study of the support of a Laurent series in several variables which is algebraic over the ring of power series over a characteristic zero field. Our fir…
Remarks on Artin approximation with constraints
Dorin Popescu, Guillaume Rond
We study various approximation results of solutions of equations where and and are two sets of variables, and where some component…
Linear nested Artin approximation theorem for algebraic power series
Francisco-Jesus Castro-Jiménez, Dorin Popescu, Guillaume Rond
We give a new and elementary proof of the nested Artin approximation Theorem for linear equations with algebraic power series coefficients. Moreover, for any Noetherian local subri…
Artin Approximation
Guillaume Rond
In 1968, M. Artin proved that any formal power series solution of a system of analytic equations may be approximated by convergent power series solutions. Motivated by this result…
Local zero estimates and effective division in rings of algebraic power series
Guillaume Rond
We give a necessary condition for algebraicity of finite modules over the ring of formal power series. This condition is given in terms of local zero estimates. In fact we show tha…
About the algebraic closure of the field of power series in several variables in characteristic zero
Guillaume Rond
We construct algebraically closed fields containing an algebraic closure of the field of power series in several variables over a characteristic zero field. Each of these fields de…
Asymptotic behaviour of standard bases
Guillaume Rond
We prove here that the elements of any standard basis of , where is an ideal of a Noetherian local ring and is a positive integer, have order bounded by a linear funct…
The Abhyankar-Jung Theorem
Adam Parusinski, Guillaume Rond
We show that every quasi-ordinary Weierstrass polynomial $P(Z) = Z^d+a_1 (X) Z^{d-1}+...+a_d(X) \in \K[[X]][Z] $, , over an algebraically closed field of characte…
An algebraic proof of Gabrielov's theorem about analytic homomorphisms in any characteristic
Guillaume Rond
The proof of proposition 3.6 is not correct
Homomorphisms of local algebras in positive characteristic
Guillaume Rond
We investigate some properties of regularity of homomorphisms of local algebras over positive characteristic fields. We state a result of monomialization of such a homomorphism bet…