论文标题
循环$ p^n $ - 特征$ p $的galois脚手架
Galois scaffolds for cyclic $p^n$-extensions in characteristic $p$
论文作者
论文摘要
令$ k $为特征$ p $的本地字段，让$ l/k $成为完全受到的galois扩展名，以便gal $（l/k）\ cong c_ c_ {p^n} $。在本文中，我们发现$ l/k $的足够条件可以接纳Galois脚手架。这为整数$ o_l $的环带来了足够的条件，使其在其关联订单$ a_0 $上没有等级1，并且更严格的条件，这意味着$ a_0 $是组环$ k [c_ {p^n}] $中的hopf订单。
Let $K$ be a local field of characteristic $p$ and let $L/K$ be a totally ramified Galois extension such that Gal$(L/K)\cong C_{p^n}$. In this paper we find sufficient conditions for $L/K$ to admit a Galois scaffold. This leads to sufficient conditions for the ring of integers $O_L$ to be free of rank 1 over its associated order $A_0$, and to stricter conditions which imply that $A_0$ is a Hopf order in the group ring $K[C_{p^n}]$.
