We give a new, sharpened version of the period theorem of Masser and Wüstholz, which is moreover totally explicit. We also present a new formulation involving all archimedean places. We then derive new bounds for elliptic isogenies, improving those of Pellarin. The small numerical constants obtained allow an application to Serre’s uniformity problem in the split Cartan case, thanks to the work of Bilu, Parent and Rebolledo.
Cite this article
Éric Gaudron, Gaël Rémond, Théorème des périodes et degrés minimaux d'isogénies. Comment. Math. Helv. 89 (2014), no. 2, pp. 343–403DOI 10.4171/CMH/322