论文标题
Morava $ k $的稳定合作 - 理论和正式小组法律群体的纤维产品
The stable cooperations of Morava $K$-Theory and the fiber product of automorphism groups of formal group laws
论文作者
论文摘要
以前有许多关于Hopf代数$ K（n）_*（k（n））$的研究，这是$ n $ th Morava $ k $的稳定合作，这是一个奇数prime的理论。尽管$ k（n）_*（k（n））$ corepresents的主要部分由本田正式的高度$ n $的正式群体定律组成的群体价值函数，$ k（n）_*（n）_*（k（n））$的整体关系之间的关系尚未得到调查。首先，我们构成了函数$ c（ - ）$，它是由正式组法的自动形态亚组和霍普夫代数$ c _*$ core corepressenting $ c（ - ）$之间的两种天然同构的纤维产物给出的。接下来，我们构建一个Hopf代数同构$κ^*：C _*\ to K（n）_*（k（n））$自然。为了将$ c _*$与$ k（n）_*（k（n））$相关联，我们使用Boardman介绍的稳定comodule代数。从Würgler和Yagita给出的$ k（n）_*（k（n））$的代数结构中，我们看到$κ^*$是同构的。由于我们通过使用正式的组法制定$ c _*$，因此同构$κ^*$阐明了$ k（n）_*（k（n））$的Hopf代数结构之间的关系，包括外部代数部分和正式小组法律。
There are many previous studies on the Hopf algebra $K(n)_*(K(n))$, the stable cooperations of $n$th Morava $K$-theory at an odd prime. Whereas the main part of $K(n)_*(K(n))$ corepresents the group-valued functor consisting of strict automorphisms of the Honda formal group law of height $n$, relations between the whole structure of $K(n)_*(K(n))$ including the exterior part and formal group laws have not been investigated well. Firstly, we constitute a functor $C(-)$ which is given by the fiber product of two natural homomorphism between subgroups of automorphisms of formal group laws, and the Hopf algebra $C_*$ corepresenting $C(-)$. Next, we construct a Hopf algebra homomorphism $κ^*:C_*\to K(n)_*(K(n))$ naturally. To relate $C_*$ to $K(n)_*(K(n))$, we use stable comodule algebras which are introduced by Boardman. From the algebra structure of $K(n)_*(K(n))$ which is given by Würgler and Yagita, we see that $κ^*$ is an isomorphism. Since we formulate $C_*$ by using formal group laws, the isomorphism $κ^*$ clarifies relationship between the Hopf algebra structure of $K(n)_*(K(n))$ including the exterior algebra part and formal group laws.
