Dans la première partie de ce texte, on établit au moyen de l’application de Manin un énoncé de finitude reliant les sections d’un schéma elliptique et les solutions des équations de Painlevé VI. Le reste de l’article concerne le théorème du noyau de Manin dans le cadre d’un schéma abélien sur une courbe, et passe en revue les divers énoncés connus sous cette appellation.
In the first part of the paper, we use Manin’s map to establish a finiteness result linking rational sections of an elliptic scheme and solutions of Painlevé VI equations. The rest of the paper concerns abelian schemes over curves, and presents a survey of the various statements encompassed by Manin’s theorem of the kernel.
Mots clés : abelian varieties, Manin maps, Gauss–Manin connections, Mumford–Tate groups, Painlevé VI equations
Daniel Bertrand 1
CC-BY 4.0
@article{AFST_2020_6_29_5_1301_0,
author = {Daniel Bertrand},
title = {Revisiting {Manin{\textquoteright}s} theorem of the kernel},
journal = {Annales de la Facult\'e des sciences de Toulouse : Math\'ematiques},
pages = {1301--1318},
publisher = {Universit\'e Paul Sabatier, Toulouse},
volume = {Ser. 6, 29},
number = {5},
year = {2020},
doi = {10.5802/afst.1662},
language = {en},
url = {https://afst.centre-mersenne.org/articles/10.5802/afst.1662/}
}
TY - JOUR AU - Daniel Bertrand TI - Revisiting Manin’s theorem of the kernel JO - Annales de la Faculté des sciences de Toulouse : Mathématiques PY - 2020 SP - 1301 EP - 1318 VL - 29 IS - 5 PB - Université Paul Sabatier, Toulouse UR - https://afst.centre-mersenne.org/articles/10.5802/afst.1662/ DO - 10.5802/afst.1662 LA - en ID - AFST_2020_6_29_5_1301_0 ER -
%0 Journal Article %A Daniel Bertrand %T Revisiting Manin’s theorem of the kernel %J Annales de la Faculté des sciences de Toulouse : Mathématiques %D 2020 %P 1301-1318 %V 29 %N 5 %I Université Paul Sabatier, Toulouse %U https://afst.centre-mersenne.org/articles/10.5802/afst.1662/ %R 10.5802/afst.1662 %G en %F AFST_2020_6_29_5_1301_0
Daniel Bertrand. Revisiting Manin’s theorem of the kernel. Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 29 (2020) no. 5, pp. 1301-1318. doi : 10.5802/afst.1662. https://afst.centre-mersenne.org/articles/10.5802/afst.1662/
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