论文标题
全局功能字段的循环扩展的理想班级组的歼灭者
Annihilators of the ideal class group of a cyclic extension of a global function field
论文作者
论文摘要
令$ k $为全球功能字段，并修复$ k $的$ \ infty $。令$ l/k $为有限的真正的Abelian扩展名，即有限的Abelian扩展名，以便$ \ infty $完全在$ l $中分配。然后，我们定义一组椭圆形单元$ c_l $中的$ \ Mathcal {o} _l^\ times $类似于Sinnott的环形单元，并计算索引$ [\ Mathcal {o} _l^\ times：c_l] $。在本文的第二部分中，我们还假设$ l $是Prime Power学位的循环扩展。然后，我们可以使用Greither和Kučera的方法来扎根这些椭圆形单元的某些根，并证明了$ l $ class Group的$ p $部分的结果。
Let $K$ be a global function field and fix a place $\infty$ of $K$. Let $L/K$ be a finite real abelian extension, i.e. a finite, abelian extension such that $\infty$ splits completely in $L$. Then we define a group of elliptic units $C_L$ in $\mathcal{O}_L^\times$ analogously to Sinnott's cyclotomic units and compute the index $[\mathcal{O}_L^\times:C_L]$. In the second part of this article, we additionally assume that $L$ is a cyclic extension of prime power degree. Then we can use the methods from Greither and Kučera to take certain roots of these elliptic units and prove a result on the annihilation of the $p$-part of the class group of $L$.
