Greenberg approximation and the geometry of arc spaces

2009/01/13 by Nicaise, Johannes, Sebag, Julien
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.0901.1806

Abstract

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.

Related

• Rationally generated arcs
• The Drinfeld-Grinberg-Kazhdan theorem and embedding codimension of the arc space
• Formal neighborhoods in arc spaces
• Geometry on arc spaces of algebraic varieties
• A Remark on Higher Homotopy Sheaves of Derived Arc Spaces