Comptes Rendus
no. 2
Algebraic geometry
On the kernel of the regulator map
[Sur le noyau de l'application régulateur]

Présenté par : Claire Voisin

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

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.

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.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2017.01.006
Sen Yang 1

1 Yau Mathematical Sciences Center, Tsinghua University, Beijing, China 
@article{CRMATH_2017__355_2_211_0,
     author = {Sen Yang},
     title = {On the kernel of the regulator map},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {211--215},
     publisher = {Elsevier},
     volume = {355},
     number = {2},
     year = {2017},
     doi = {10.1016/j.crma.2017.01.006},
     language = {en},
}
TY  - JOUR
AU  - Sen Yang
TI  - On the kernel of the regulator map
JO  - Comptes Rendus. Mathématique
PY  - 2017
SP  - 211
EP  - 215
VL  - 355
IS  - 2
PB  - Elsevier
DO  - 10.1016/j.crma.2017.01.006
LA  - en
ID  - CRMATH_2017__355_2_211_0
ER  - 
%0 Journal Article
%A Sen Yang
%T On the kernel of the regulator map
%J Comptes Rendus. Mathématique
%D 2017
%P 211-215
%V 355
%N 2
%I Elsevier
%R 10.1016/j.crma.2017.01.006
%G en
%F CRMATH_2017__355_2_211_0
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

Cité par Sources :

Commentaires - Politique