The differential Galois group of the maximal prounipotent extension is free

The differential Galois group of the maximal prounipotent extension is free
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最大原能扩张的微分伽罗瓦群是自由的

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发表时间：
2020
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通讯作者：
A. Magid
A. Magid
中科院分区：
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文献类型：
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作者：
A. Magid

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设F是一个具有代数闭常数域的特征零微分域，考虑F的所有Picard-Vessiot扩张与幂幺微分Galois群的合成F_u。本文证明了F_u的F微分自同构群是自由的prounipotent群。
Let $F$ be a characteristic zero differential field with algebraically closed constant field, and consider the compositum $F_u$ of all Picard--Vessiot extensions of $F$ with unipotent differential Galois group. We prove that the group of $F$ differential automorphisms of $F_u$ is a free prounipotent group.