Nash triviality in families of Nash mappings
Annales de l'Institut Fourier, Volume 51 (2001) no. 5, p. 1209-1228

We study triviality of Nash families of proper Nash submersions or, in a more general setting, the triviality of pairs of proper Nash submersions. We work with Nash manifolds and mappings defined over an arbitrary real closed field R. To substitute the integration of vector fields, we study the fibers of such families on points of the real spectrum R p ˜ and we construct models of proper Nash submersions over smaller real closed fields. Finally we obtain results on finiteness of topological types in families of Nash mappings, and also results on effectiveness of the above constructions.

On étudie des résultats de trivialité pour les familles de Nash de submersions de Nash propres. On travaille avec des variétés et des applications de Nash définies sur un corps réel clos quelconque R. Pour éviter l’usage de l’intégration des champs de vecteurs (processus non algébrique en général), on étudie les fibres de telles familles sur les points appartenant au spectre réel R p ˜, et on construit des modèles de submersions de Nash propres sur des corps réels clos plus petits. Finalement, on obtient des résultats de finitude sur le type topologique des familles d’applications de Nash, et aussi des résultats sur l’effectivité de telles constructions.

DOI : https://doi.org/10.5802/aif.1852
Classification:  14P20,  58A07
Keywords: Nash manifold, Nash mapping, Nash triviality, real spectrum
@article{AIF_2001__51_5_1209_0,
     author = {Escribano, Jes\'us},
     title = {Nash triviality in families of Nash mappings},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {51},
     number = {5},
     year = {2001},
     pages = {1209-1228},
     doi = {10.5802/aif.1852},
     zbl = {0979.14026},
     mrnumber = {1860663},
     language = {en},
     url = {http://www.numdam.org/item/AIF_2001__51_5_1209_0}
}
Escribano, Jesús. Nash triviality in families of Nash mappings. Annales de l'Institut Fourier, Volume 51 (2001) no. 5, pp. 1209-1228. doi : 10.5802/aif.1852. http://www.numdam.org/item/AIF_2001__51_5_1209_0/

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