The Grothendieck ring of varieties is not a domain
By Bjorn Poonen. 2002
107 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/9950f6b14ae76dd92b1a4a3593cbc08fe047a92b
How researchers see this paper
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In Algebra and Number Theory
- Julien Sebag
- Johannes Nicaise
- Qing Liu
- Michael Stoll
- Matthew Baker
- Dino J. Lorenzini
- Joseph Rabinoff
- M. Kerz
In Computational Theory and Mathematics
- Julien Sebag
- Johannes Nicaise
- Qing Liu
- Michael Stoll
- Matthew Baker
- Dino J. Lorenzini
- Joseph Rabinoff
- M. Kerz
In Geometry and Topology
- Johannes Nicaise
- Julien Sebag
- Qing Liu
- M. Temkin
- L. H. Halle
- Michael Stoll
- Matthew Baker
- Dino J. Lorenzini
Citations in the corpus
- The Grothendieck ring of varieties and piecewise isomorphisms (2010, background): “This property is a key point in the proof of [33], Theorem 1.”
- Motivic Serre invariants, ramification, and the analytic Milnor fiber (2007, background): “In this setting, the notion of pole has to be defined with care [41, §4], since the Grothendieck ring of varieties is not a domain [40].”