no. 9
Algebraic geometry
The class of the affine line is a zero divisor in the Grothendieck ring: An improvement
[La classe de la droite affine est un diviseur de zéro dans l'anneau de Grothendieck : une amélioration]

Présenté par : Claire Voisin

Martin, Nicolas1
1 Centre de mathématiques Laurent-Schwartz, École polytechnique, 91128 Palaiseau cedex, France
Comptes Rendus. Mathématique, Tome 354 (2016) no. 9, pp. 936-939.

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2016.05.016
Martin, Nicolas 1

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

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

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

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

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