no. 10
Logic/Algebraic geometry
A proof of the integral identity conjecture, II
[Une preuve de la conjecture de l'identité intégrale, II]

Présenté par : Claire Voisin

Lê, Quy Thuong1, 2 
1 Department of Mathematics, Vietnam National University, 334 Nguyen Trai Street, Hanoi, Viet Nam
2 Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain
Comptes Rendus. Mathématique, Tome 355 (2017) no. 10, pp. 1041-1045.

Dans cette note, en utilisant la théorie de l'intégration motivique de Cluckers et Loeser, nous prouvons la conjecture de l'identité intégrale dans le cadre d'un anneau de Grothendieck de variétés localisé sur un corps arbitraire de caractéristique nulle.

In this note, using Cluckers–Loeser's theory of motivic integration, we prove the integral identity conjecture with framework a localized Grothendieck ring of varieties over an arbitrary base field of characteristic zero.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.10.005
Lê, Quy Thuong 1, 2

1 Department of Mathematics, Vietnam National University, 334 Nguyen Trai Street, Hanoi, Viet Nam
2 Basque Center for Applied Mathematics, Alameda de Mazarredo 14, 48009 Bilbao, Basque Country, Spain 
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Lê, Quy Thuong. A proof of the integral identity conjecture, II. Comptes Rendus. Mathématique, Tome 355 (2017) no. 10, pp. 1041-1045. doi : 10.1016/j.crma.2017.10.005. http://www.numdam.org/articles/10.1016/j.crma.2017.10.005/

[1] Cluckers, R.; Loeser, F. Constructible motivic functions and motivic integration, Invent. Math., Volume 173 (2008) no. 1, pp. 23-121

[2] Denef, J.; Loeser, F. Motivic Igusa zeta functions, J. Algebraic Geom., Volume 7 (1998), pp. 505-537

[3] Denef, J.; Loeser, F. Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math., Volume 135 (1999), pp. 201-232

[4] Kontsevich, M.; Soibelman, Y. Stability structures, motivic Donalson–Thomas invariants and cluster tranformations | arXiv

[5] Lê, Q.T. On a conjecture of Kontsevich and Soibelman, Algebra Number Theory, Volume 6 (2012) no. 2, pp. 389-404

[6] Lê, Q.T. Proofs of the integral identity conjecture over algebraically closed fields, Duke Math. J., Volume 164 (2015) no. 1, pp. 157-194

[7] Nicaise, J.; Payne, S. A tropical motivic Fubini theorem with applications to Donaldson–Thomas theory | arXiv

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