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The Grothendieck ring of varieties is not a domain

Bjorn Poonen
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Abstract

Let k be a field. Let K_0(V_k) denote the quotient of the free abelian group generated by the geometrically reduced varieties over k, modulo the relations of the form [X]=[X-Y]+[Y] whenever Y is a closed subvariety of X. Product of varieties makes K_0(V_k) into a ring. We prove that if the characteristic of k is zero, then K_0(V_k) is not a domain.

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Bjorn Poonen. 2002-04-24. The Grothendieck ring of varieties is not a domain. https://doi.org/10.4310/mrl.2002.v9.n4.a8

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