Serre's uniformity problem in the split Cartan case

• 成果类型: Article
• 署名作者: Bilu, Yuri; Parent, Pierre
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• DOI: 10.4007/annals.2011.173.1.13
• 发表日期: 2011
• 页码: 569-584
• 关键词: galois properties; rational-points; normalizers; isogenies; SUBGROUPS

摘要

We prove that there exists an integer p(0) such that X-split(p)(Q) is made of cusps and CM-points for any prime p > p(0). Equivalently, for any non-CM elliptic curve E over Q and any prime p > po the image of Gal((Q) over bar /Q) by the representation induced by the Galois action on the p-division points of E is not contained in the normalizer of a split Cartan subgroup. This gives a partial answer to an old question of Serre.