On the theory of commutative formal groups
On the theory of commutative formal groups
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论交换形式群理论
DOI：
10.2969/jmsj/02220213
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发表时间：
1970
影响因子：
0.7
通讯作者：
T. Honda
中科院分区：
文献类型：
--
作者：
T. Honda
（交换）形式群的理论是由M. Lazard和J. Dieudonne在1954年左右。Lazard [11]，[12]通过显式处理幂级数的系数，研究了任意交换环上的交换形式群。而Dieudonn 'e专门研究了特征为p>0的域上的形式群.他在[4]中减少了对特征为$p>0$的完美域上的交换形式群的研究，使其成为对某个非交换环上的模的研究，即所谓的Dieudonn\'e模，并在[5]中得到了特征为$p>0$的代数闭域上的交换形式群的同构类的完整分类。后来Manin [16]研究了简单形式群的同构类。Lubin [13]开始研究$\mathfrak{p}$ -adic整数环上的X-维形式群，他和Tate得到了一些有趣的结果。本文首先构造了p-adic整数环上任意维数的交换形式群的一般族。在环上
The theory of (commutative) formal groups was initiated by M. Lazard and J. Dieudonne around 1954. Lazard [11], [12] studied commutative formal groups over an arbitrary commutative ring by treating the coefficients of power series explicitly. Whereas Dieudonn\’e investigated formal groups over a field of characteristic $p>0$ exclusively. He reduced in [4] the study of commutative formal groups over a perfect field of characteristic $p>0$ to that of modules over a certain non-commutative ring, so-called Dieudonn\’e modules, and obtained in [5] a complete classification of isogeny classes of commutative formal groups over an algebraically closed field of characteristic $p>0$ . Later Manin [16] studied isomorphism classes of simple formal groups. The study of Xone-dimensional formal groups over $\mathfrak{p}$ -adic integer rings was begun by Lubin [13] and a number of interesting results were obtained by him and Tate. In this paper we first construct a certain general family of commutative formal groups of arbitrary dimension over a p-adic integer ring. Over the ring