GROTHENDIECK RINGS OF DEFINABLE SUBASSIGNMENTS AND EQUIVARIANT MOTIVIC MEASURES - Le, Quy Thuong (Trường Đại học Đà Lạt, 2023)
This paper studies categories of definable subassignments with some category equivalences to semi-algebraic and constructible subsets of arc spaces of algebraic varieties. These equivalences lead to the identity of certain Grothendieck rings, which allows us to compare the motivic measure of Cluckers-Loeser with that of Denef-Loeser for certain classes of definable subassignments.