Local uniformization and arc spaces

Olivier Piltant (1) , Ana J Reguera (2)

1 LMV - Laboratoire de Mathématiques de Versailles
2 Dep. Álgebra, Análisis Matemático, Geometría y Topología,

Let X be a variety over a perfect field k and let X_∞ be its space of arcs. We prove that Local Uniformization on X implies that, for every closed subset Z of X, the closed subset of X_∞ consisting of all arcs centered at some point of Z has a finite number of irreducible componets. This strenghens a theorem due to J. Nash.

Mots clés: Space of arcs; Local Uniformization

Domaines: Mathématiques [math]

Olivier Piltant, Ana J Reguera. Local uniformization and arc spaces. Journal of Pure and Applied Algebra, 2018, ⟨10.1016/j.jpaa.2017.08.012⟩. ⟨hal-01379692⟩