Field Theory for Function Fields of Plane Quartic Curves
Field Theory for Function Fields of Plane Quartic Curves
复制标题
平面四次曲线函数场的场论
DOI：
10.1006/jabr.1999.8173
复制
发表时间：
2000
影响因子：
0.9
通讯作者：
Hisao Yoshihara
中科院分区：
文献类型：
--
作者：
Kei Miura;Hisao Yoshihara
设C是域k上的光滑平面四次曲线，k(C)是C的有理函数场，我们用下面的方法发展了k(C)的场论。设πP是从C到一条L直线的投影，其中心P为∈和P2.πP诱导出一个扩域k(C)/k(P1)，其中k(P1)是极大有理子域.本文从几个角度研究了扩张k(C)/k(P1)。例如，我们考虑以下问题：扩张k(C)/k(P 1)Galois是什么时候？K(C)/k(P1)的Galois闭包是什么？
Abstract Let C be a smooth plane quartic curve over a field k and k(C) be a rational function field of C. We develop a field theory for k(C) in the following method. Let πP be the projection from C to a line l with a center P ∈ P 2. The πP induces an extension field k(C)/k( P 1), where k( P 1) is a maximal rational subfield. In this paper we study the extension k(C)/k( P 1) from several points of view. For example, we consider the following questions: When is the extension k(C)/k( P 1) Galois? What is the Galois closure of k(C)/k( P 1)?