论文标题
Hopf Galois模块的二面步结构$ 2P $ $ \ MATHBB {q} _p $的扩展
Hopf Galois module structure of dihedral degree $2p$ extensions of $\mathbb{Q}_p$
论文作者
论文摘要
令$ p $是一个奇怪的素数。对于现场扩展，$ l/\ mathbb {q} _p $与galois组同构为二面体$ d_ {2p} $ of $ 2p $的$ d_ {2p} $，我们考虑计算每个hopf galois结构中相关顺序的问题的问题我们解决了$ l/\ mathbb {q} _p $的情况，并未完全分解，并提出了一种实用方法，该方法为$ p = 3 $和$ p = 5 $提供了完整的答案。我们看到，在这个二面积的延伸家族中，整数在不同的Hopf Galois结构中的相关顺序始终是自由的。
Let $p$ be an odd prime. For field extensions $L/\mathbb{Q}_p$ with Galois group isomorphic to the dihedral group $D_{2p}$ of order $2p$, we consider the problem of computing a basis of the associated order in each Hopf Galois structure and the module structure of the ring of integers $\mathcal{O}_L$. We solve the case in which $L/\mathbb{Q}_p$ is not totally ramified and present a practical method which provides a complete answer for the cases $p=3$ and $p=5$. We see that within this family of dihedral extensions, the ring of integers is always free over the associated orders in the different Hopf Galois structures.
