%0 Journal Article
%T Progr¨¨s r¨¦cents sur les fonctions normales (d'apr¨¨s Green-Griffiths, Brosnan-Pearlstein, M. Saito, Schnell...)
%A Fran£¿ois Charles
%J Mathematics
%D 2013
%I arXiv
%X Given a family of smooth complex projective varieties, the Hodge conjecture predicts the algebraicity of the locus of Hodge classes. This was proven unconditionnally by Cattani, Deligne and Kaplan in 1995. In a similar way, conjectures on algebraic cycles have led Green and Griffiths to conjecture the algebraicity of the zero locus of normal functions. This corresponds to a mixed version of the theorem of Cattani, Deligne and Kaplan. This result has been proven recently by Brosnan-Pearlstein, Kato-Nakayama-Usui, and Schnell building on work of M. Saito. We will present some of the ideas around this theorem.
%U http://arxiv.org/abs/1301.7235v1