论文标题
在$ \ mathbb {p}^1 $的属的定义领域
On the fields of definition of genus-one covers of $\mathbb{P}^1$
论文作者
论文摘要
众所周知，有时在其模量领域没有定义Belyi对。取而代之的是，它是根据其模量字段的有限程度扩展定义的，称为定义字段。我们表明，鉴于一个数字$ m $，存在一对，使得Moduli领域的定义领域程度大于$ M $。作为副产品，我们获得了Belyi对的局部全球原理的反例。
It is known that sometimes a Belyi pair is not defined over its field of moduli. Instead, it is defined over a finite degree extension of its field of moduli, called a field of definition. We show that given a number $m$ there exists a Belyi pair such that the degree of a field of definition over the field of moduli is greater than $m$. As a byproduct, we obtain a counterexample to the local-global principle for Belyi pairs.
