Let $K\_0(Var\_k)$ be the grothendieck group of the category of $k$-varieties, and call its elements virtual motives. $\mathbb{L}:=[\mathbb{A}^1\_k]$ is called the Lefschetz motive. I think that if a virtual motive is divisible by arbitrarily high powers of $\mathbb{L}$, then it must be $0$. Is this true? If so, is there a proof of this?



Virtual Motives Infinitely Divisible by Lefschetz Motive
This is an open problem. It's probably quite hard.


