Comptes Rendus
no. 9
Algebraic geometry
The class of the affine line is a zero divisor in the Grothendieck ring: An improvement

Presented by: Claire Voisin

Nicolas Martin1
1 Centre de mathématiques Laurent-Schwartz, École polytechnique, 91128 Palaiseau cedex, France
Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 936-939.

Lev A. Borisov has shown that the class of the affine line is a zero divisor in the Grothendieck ring of algebraic varieties over complex numbers. We improve the final formula by removing a factor.

Lev A. Borisov a prouvé que la classe de la droite affine est un diviseur de zéro dans l'anneau de Grothendieck des variétés algébriques complexes. Nous améliorons la formule finale en supprimant un facteur.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2016.05.016

Nicolas Martin 1

1 Centre de mathématiques Laurent-Schwartz, École polytechnique, 91128 Palaiseau cedex, France 
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Nicolas Martin. The class of the affine line is a zero divisor in the Grothendieck ring: An improvement. Comptes Rendus. Mathématique, Volume 354 (2016) no. 9, pp. 936-939. doi : 10.1016/j.crma.2016.05.016. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2016.05.016/

[1] L. Borisov The class of the affine line is a zero divisor in the Grothendieck ring, 2014 | arXiv

[2] M. Larsen; V. Lunts Motivic measures and stable birational geometry, Mosc. Math. J., Volume 3 (2003) no. 1, pp. 85-95

[3] B. Poonen The Grothendieck ring of varieties is not a domain, Math. Res. Lett., Volume 9 (2002) no. 4, pp. 493-497

[4] E. Rødland The Pfaffian Calabi–Yau, its mirror, and their link to the Grassmannian G(2, 7), Compos. Math., Volume 122 (2000) no. 2, pp. 135-149

[5] J. Sebag Intégration motivique sur les schémas formels, Bull. Soc. Math. Fr., Volume 132 (2004) no. 1, pp. 1-54

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