GROTHENDIECK RINGS OF DEFINABLE SUBASSIGNMENTS AND EQUIVARIANT MOTIVIC MEASURES
DOI:
https://doi.org/10.37569/DalatUniversity.12.2.902(2022)Keywords:
Definable subassignments, Grothendieck ring, Measurable subassignments, Motivic measure.Abstract
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.
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