The Grothendieck ring of varieties is not a domain
Algebraic Geometry
2017-04-03 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.math/0204306,
title = {The Grothendieck ring of varieties is not a domain},
author = {Bjorn Poonen},
journal= {arXiv preprint arXiv:math/0204306},
year = {2017}
}
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4 pages