3 citations · 4 across the 4 of their papers we have counts for
5 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…
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…
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…
An algebraic proof of Gabrielov's theorem about analytic homomorphisms in any characteristic
Guillaume Rond
The proof of proposition 3.6 is not correct