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 ?

  • $\begingroup$ What do you mean by "Vec" here? $\endgroup$ – Vladimir Dotsenko Jul 26 '16 at 17:56
  • 2
    $\begingroup$ Sorry, it should be $\mathbf{Var}$ - category of quasi-projective varieties over given field $k$. $\endgroup$ – mikis Jul 26 '16 at 17:58

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