形式群的自同构群的外在性质
Extrinsic properties of automorphism groups of formal groups
摘要：
本文证明了定义在正特征域上的一维形式群律的自同构群的两个定理。第一个是，如果一个级数与形式群律的一个非挠自同构交换，那么这个级数已经是一个自同构。第二个是自同构群在基域上的可逆级数群中是它自己的正规化子。这些结果的一个推论是：一个正特征的形式群律由它的任何一个非挠自同构决定。
英文摘要：
We prove two conjectures on the automorphism group of a one-dimensional formal group law defined over a field of positive characteristic. The first is that if a series commutes with a nontorsion automorphism of the formal group law, then that series is already an automorphism. The second is that the group of automorphisms is its own normalizer in the group of all invertible series over the ground field. A consequence of these results is that a formal group law in positive characteristic is determined by any one of its nontorsion automorphisms.
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