Progrès récents sur les fonctions normales (d'après Green-Griffiths, Brosnan-Pearlstein, M. Saito, Schnell...)
arXiv:1301.7235
Abstract
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.
30 p., séminaire Bourbaki, 65ème année, 2012-2013, exp. 1063. Comments welcome