Weierstrass preparation theorem and singularities in the space of non-degenerate arcs

19 Jun 2017 · Chau Ngo Bao ·

We study the Weierstrass preparation and division theorems over arbitrary test rings and the local structure of singularities in the space of nondegenerate arcs on algebraic varieties. As an application, we prove a strengthened version of a theorem of Grinberg-Kazhdan and Drinfeld.