AI 中文总结
本文在特征3下建立了拟椭圆曲面整体截面的挠秩与超椭圆曲线p-秩的联系，并据此确定了一类拟椭圆曲面Mordell--Weil群的挠秩。
AI 中文摘要
在特征$p=3$时，我们建立了射影直线${\mathbf P}^1$上拟椭圆曲面的整体截面的初等阿贝尔群的挠秩与某些超椭圆曲线的$p$-秩之间的具体关系，从而解释了I. Dolgachev先前观察到的这两个不变量之间的神秘关系。作为应用，我们确定了一类拟椭圆曲面的Mordell--Weil群的挠秩。
英文摘要
In characteristic $p =3$, we establish a concrete relationship between the torsion rank of the elementary abelian group of global sections of quasi-elliptic surfaces over the projective line ${\mathbf P}^1$ and the $p$-rank of certain hyperelliptic curves, thereby explaining a mysterious relationship between these two invariants previously observed by I. Dolgachev. As an application, we determine the torsion ranks of the Mordell--Weil groups of a class of quasi-elliptic surfaces.
Comments13 pages
