# Properties of Grothendieck ring for field of characterictic $p$

In this article there is a proof that for field $k$ of characteristic zero Grothendieck ring $K(\mathbf{Var}_k)$ is not an integral domain. In many articles I found statement that similar theorem for field of characteristic $p$ is unknown. These articles have at least five years. My question is : Are there some new developments in this area ?

• What do you mean by "Vec" here? – Vladimir Dotsenko Jul 26 '16 at 17:56
• Sorry, it should be $\mathbf{Var}$ - category of quasi-projective varieties over given field $k$. – mikis Jul 26 '16 at 17:58