A remark on Berger's conjecture, Kolchin's theorem, and arc schemes

摘要

Let k be a field of characteristic zero. Let V be a k-scheme of finite type, i.e., a k-variety, which is integral. We prove that if the associated arc scheme is reduced, then the -Module is torsion-free. Then if the k-variety V is assumed to be locally a complete intersection (lci), we deduce that the k-variety V is normal. We also obtain the following consequence: for every class of integral k-curves which satisfies the Berger conjecture, and for every , the k-curve is smooth if and only if is reduced.