3 citations · 4 across the 4 of their papers we have counts for
11 papers
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…
Preordered groups and valued fields
Julie Decaup, Guillaume Rond
We study algebraic, combinatorial and topological properties of the set of preorders on a group, and the set of valuations on a field. We show strong analogies between these two ki…
Transcendental holomorphic maps between real algebraic manifolds in a complex space
Guillaume Rond
We give an example of a real algebraic manifold embedded in a complex space that does not satisfy the Nash-Artin approximation Property. This Nash-Artin approximation Property is c…
Algebraic varieties are homeomorphic to varieties defined over number fields
Adam Parusinski, Guillaume Rond
We show that every affine or projective algebraic variety defined over the field of real or complex numbers is homeomorphic to a variety defined over the field of algebraic numbers…
Multiparameter perturbation theory of matrices and linear operators
Adam Parusinski, Guillaume Rond
We show that a normal matrix with coefficient in , , can be diagonalized, provided the discriminant of its characteristic polynomia…