当前位置: X-MOL 学术Int. J. Number Theory › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Triples of singular moduli with rational product
International Journal of Number Theory ( IF 0.5 ) Pub Date : 2020-06-12 , DOI: 10.1142/s1793042120501110
Guy Fowler 1
Affiliation  

We show that all triples [Formula: see text] of singular moduli satisfying [Formula: see text] are “trivial”. That is, either [Formula: see text]; some [Formula: see text] and the remaining [Formula: see text] are distinct, of degree [Formula: see text], and conjugate over [Formula: see text]; or [Formula: see text] are pairwise distinct, of degree [Formula: see text], and conjugate over [Formula: see text]. This theorem is best possible and is the natural three-dimensional analogue of a result of Bilu, Luca and Pizarro-Madariaga in two dimensions. It establishes an explicit version of the André–Oort conjecture for the family of subvarieties [Formula: see text] defined by an equation [Formula: see text].

中文翻译:

有理积的奇异模的三元组

我们证明满足[公式:见文本]的奇异模的所有三元组[公式:见文本]都是“微不足道的”。即[公式:见正文];一些[公式:见文]和其余的[公式:见文]是不同的,程度[公式:见文],共轭[公式:见文];或 [Formula: see text] 是成对不同的,度数 [Formula: see text],并且在 [Formula: see text] 上共轭。这个定理是最好的,并且是 Bilu、Luca 和 Pizarro-Madariaga 在二维中的结果的自然三维模拟。它为由方程[公式:见文本]定义的子变体族[公式:见文本]建立了安德烈-奥尔特猜想的显式版本。
更新日期:2020-06-12
down
wechat
bug