Comptes Rendus
no. 2
Algebraic geometry
On the kernel of the regulator map

Presented by: Claire Voisin

Sen Yang1
1 Yau Mathematical Sciences Center, Tsinghua University, Beijing, China
Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 211-215.

By using the infinitesimal methods due to Bloch, Green, and Griffiths in [1,4], we construct an infinitesimal form of the regulator map and verify that its kernel is ΩC/Q1, which suggests that Question 1.1 seems reasonable at the infinitesimal level.

Utilisant les méthodes infinitésimales dues à Bloch, Green et Griffiths [1,4], nous construisons une forme infinitésimale de l'application régulateur. Nous vérifions que son noyau est ΩC/Q1, ce qui suggère une version infinitésimale valide de la Question 1.1 formulée dans le texte.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2017.01.006

Sen Yang 1

1 Yau Mathematical Sciences Center, Tsinghua University, Beijing, China 
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Sen Yang. On the kernel of the regulator map. Comptes Rendus. Mathématique, Volume 355 (2017) no. 2, pp. 211-215. doi : 10.1016/j.crma.2017.01.006. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2017.01.006/

[1] S. Bloch The dilogarithm and extensions of Lie algebras, Northwestern Univ., Evanston, Ill., 1980 (Lect. Notes Math.), Volume vol. 854, Springer, Berlin–New York (1981), pp. 1-23

[2] M. Green Infinitesimal methods in Hodge theory, Torino, 1993 (Lect. Notes Math.), Volume vol. 1594, Springer, Berlin (1994), pp. 1-92

[3] M. Green; P. Griffiths The regulator map for a general curve, Salt Lake City, UT, 2000 (Contemp. Math.), Volume vol. 312, Amer. Math. Soc., Providence, RI (2002), pp. 117-127

[4] M. Green; P. Griffiths On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety, Ann. Math. Stud., vol. 157, Princeton University Press, Princeton, NJ, USA, 2005 vi+200 pp. (ISBN: 0-681-12044-7)

[5] R. Hain Classical polylogarithms, Seattle, WA, USA, 1991 (Proc. Symp. Pure Math.), Volume vol. 55, Amer. Math. Soc., Providence, RI, USA (1994), pp. 3-42

[6] M. Kerr An elementary proof of Suslin reciprocity, Can. Math. Bull., Volume 48 (2005) no. 2, pp. 221-236

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