7 citations · 15 across the 15 of their papers we have counts for
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math.CV2020
A proof of A. Gabrielov's rank Theorem
André Belotto da Silva, Octave Curmi, Guillaume Rond
This article contains a complete proof of Gabrielov's rank Theorem, a fundamental result in the study of analytic map germs. Inspired by the works of Gabrielov and Tougeron, we dev…
math.AC2020
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…
math.AC2020
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…