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Revisiting Manin’s theorem of the kernel
Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 29 (2020) no. 5, pp. 1301-1318.

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.

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.

Published online:
DOI: 10.5802/afst.1662
Classification: 14K05,  32G20,  11G10,  12H05,  34M55
Keywords: abelian varieties, Manin maps, Gauss–Manin connections, Mumford–Tate groups, Painlevé VI equations
Daniel Bertrand 1

1 Sorbonne Université & UMR 7586 du CNRS, Institut de Mathématiques de Jussieu-PRG, Case 247, 75 252 Paris Cédex 05, France
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights
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Daniel Bertrand. Revisiting Manin’s theorem of the kernel. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 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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