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Does the Grothendieck ring of varieties contain torsion?

As per Theo Johnson-Freyd's request, I'm converting my comment to an answer. Larsen-Lunts show that if $k$ is algebraically closed of characteristic zero, then there is a natural isomorphisms $$K_0(\ …
Daniel Litt's user avatar
4 votes

Generalized Euler characteristics of non-motivic origin

See section 7 of Bondal-Larsen-Lunt's paper "Grothendieck Ring of Pretriangulated categories, where they construct a non-trivial morphism $$\mu: K_0(\text{Var}_k)\to \mathcal{PT}$$ where the latter is …
Daniel Litt's user avatar