The Grothendieck ring of varieties is not a domain

Details The Grothendieck ring of varieties is not a domain The Grothendieck ring of varieties is not a domain

2002-04-24

arxiv.org/abs/math/0204306v1

Mathematics

Algebraic Geometry

4 pages

Scientific paper

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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