Power structures on the Grothendieck--Witt ring and the motivic Euler characteristic

Abstract

For $k$ a field, we construct a power structure on the Grothendieck--Witt ring of $k$ which has the potential to be compatible with symmetric powers of varieties and the motivic Euler characteristic. We then show this power structure is compatible with the power structure when we restrict to varieties of dimension $0$.

arXiv comment20 pages, comments welcome! Minor fixes

References in corpus (2)

• Perfection in motivic homotopy theory
• Motivic Gauß-Bonnet formulas

Cited by in corpus (1)

• Compactly supported ${\mathbb{A}}^1$-Euler characteristics of symmetric powers of cellular varieties