The Grothendieck ring of varieties is not a domain
Abstract
Let k be a field. Let K0(Vk) 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 K0(Vk) into a ring. We prove that if the characteristic of k is zero, then K0(Vk) is not a domain.
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