Soit une courbe sur un corps et soit . Nous définissons un cycle canonique . Supposons que est un corps de nombres et que a un modèle semi-stable sur les entiers de dont les composantes irréductibles des fibres sont lisses. Nous construisons un modèle régulier de et vérifions que l’accouplement de Beilinson-Bloch, , est bien défini, où et sont les correspondances. Si est une courbe modulaire et et sont les opérateurs de Hecke convenables, on conjecture une formule liant la dérivée d’une fonction avec l’accouplement de Beilinson-Bloch.
Let be a curve over a field with a rational point . We define a canonical cycle . Suppose that is a number field and that has semi-stable reduction over the integers of with fiber components non-singular. We construct a regular model of and show that the height pairing is well defined where and are correspondences. The paper ends with a brief discussion of heights and -functions in the case that is a modular curve.
@article{AIF_1995__45_3_649_0, author = {Gross, Benedict H. and Schoen, Chad}, title = {The modified diagonal cycle on the triple product of a pointed curve}, journal = {Annales de l'Institut Fourier}, pages = {649--679}, publisher = {Association des Annales de l{\textquoteright}institut Fourier}, volume = {45}, number = {3}, year = {1995}, doi = {10.5802/aif.1469}, mrnumber = {96e:14008}, zbl = {0822.14015}, language = {en}, url = {http://archive.numdam.org/articles/10.5802/aif.1469/} }
TY - JOUR AU - Gross, Benedict H. AU - Schoen, Chad TI - The modified diagonal cycle on the triple product of a pointed curve JO - Annales de l'Institut Fourier PY - 1995 SP - 649 EP - 679 VL - 45 IS - 3 PB - Association des Annales de l’institut Fourier UR - http://archive.numdam.org/articles/10.5802/aif.1469/ DO - 10.5802/aif.1469 LA - en ID - AIF_1995__45_3_649_0 ER -
%0 Journal Article %A Gross, Benedict H. %A Schoen, Chad %T The modified diagonal cycle on the triple product of a pointed curve %J Annales de l'Institut Fourier %D 1995 %P 649-679 %V 45 %N 3 %I Association des Annales de l’institut Fourier %U http://archive.numdam.org/articles/10.5802/aif.1469/ %R 10.5802/aif.1469 %G en %F AIF_1995__45_3_649_0
Gross, Benedict H.; Schoen, Chad. The modified diagonal cycle on the triple product of a pointed curve. Annales de l'Institut Fourier, Tome 45 (1995) no. 3, pp. 649-679. doi : 10.5802/aif.1469. http://archive.numdam.org/articles/10.5802/aif.1469/
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