Vakil–Wood motivic stabilization conjecture

Let $\mathcal U$ be a geometrically irreducible ungraded variety, and let $\mathcal X_n$ denote its space of effective zero-cycles of degree $n$. Write $\mathbb L$ for the Lefschetz class and let $\widehat{\mathcal M}$ be the completed Grothendieck ring. Vakil–Wood motivic stabilization conjecture. The limit

$$\lim_{n\to\infty}\frac{[\mathcal X_n]}{\mathbb L^{\dim \mathcal X_n}}$$

exists in $\widehat{\mathcal M}$. This is one of the motivic stabilization conjectures; the statement concerns convergence of normalized classes of symmetric products in the completed Grothendieck ring.