论文标题
完整的Picard船只关闭
The Complete Picard Vessiot Closure
论文作者
论文摘要
令F为具有常数C的差异场。我们假设C是代数封闭的，并且具有特征性0。完全PICARD-F的f是f的差闭合是F与F与F相同的f的差异场扩展，而F与f相同的常数，没有Picard-vessiot扩展，并且在F上与这些属性相比是最小的。完整的皮卡德（Picard）的子字段与其差异自动形态群体的子群之间有一个对应关系，这是因为完整的picard-vessiot闭合来自f通过重复的picard-vessiot扩展。该对应关系也可以获得完整的Picard闭合的某些正常子场，即可以独立于其嵌入到完整的Picard中的野外闭合的字段。
Let F be a differential field with field of constants C. We assume C to be algebraically closed and of characteristic 0. The complete Picard--Vessiot closure of F is a differential field extension of F with the same constants C as F, which has no Picard--Vessiot extensions, and is minimal over F with these properties. There is a correspondence between subfields of the complete Picard--Vessiot closure and subgroups of its differential automorphism group, which arises because the complete Picard--Vessiot closure comes from F via repeated Picard--Vessiot extensions. This correspondence also obtains for certain normal subfields of the complete Picard--Vessiot closure, fields which can be characterized independently of their embedding in the complete Picard--Vessiot closure.
