Formal Neighbourhoods and Formal Models of Non-Degenerate Arcs

An important result about the geometry of the arc space of an algebraic variety is the theorem of Drinfeld–Grinberg–Kazhdan, representing the formal neighbourhood of a non-degenerate arc. We start with a brief review of some important results and notions. Then the complete proof of the theorem with examples is given. A generalization to the relative case is discussed for smooth and ´etale morphisms.