GREENBERG APPROXIMATION AND THE GEOMETRY OF ARC SPACES

Johannes Nicaise (1) , Julien Sebag (2)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 IRMAR - Institut de Recherche Mathématique de Rennes

We study the differential properties of generalized arc schemes and geometric versions of Kolchin's Irreducibility Theorem over arbitrary base fields. As an intermediate step, we prove an approximation result for arcs by algebraic curves.

Mots clés: Algebraic geometry; Arc scheme; Differential algebra

Domaines: Géométrie algébrique [math.AG]

Johannes Nicaise, Julien Sebag. GREENBERG APPROXIMATION AND THE GEOMETRY OF ARC SPACES. Communications in Algebra, 2010, 38 (11), pp.4077-4096. ⟨10.1080/00927870903295398⟩. ⟨hal-00578779⟩