[過去ﾛｸﾞ] 現代数学の系譜 工学物理雑談 古典ガロア理論も読む78 (1002ﾚｽ)
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467(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/11/04(月)18:03 ID:Qu1TcOyQ(7/28) AAS
>>466
つづき

This was introduced in our previous paper [Leg13b] in the number
field case. Given a field k and a finite group G, the question of whether
there is a G-parametric extension over k of group G or not is intermediate between these classical two questions in inverse Galois theory:
- if there is such an extension, then it obviously solves the BeckmannBlack problem for G over k, which asks whether any Galois extension
F/k of group G occurs as a specialization of some k-regular Galois
省15

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468(1): 現代数学の系譜 雑談 古典ガロア理論も読む ◆e.a0E5TtKE 2019/11/04(月)18:04 ID:Qu1TcOyQ(8/28) AAS
>>467
つづき

1.3. A systematic approach. In §4, we offer a systematic approach,
already started in [Leg13b], to give more examples of non H-parametric
extensions over k of group G containing H. Given a k-regular Galois extension E1/k(T) of group H and a k-regular Galois extension E2/k(T)
of group G, we provide two sufficient conditions which each guarantees
that there exist some specializations of E1/k(T) of group H which cannot be specializations of E2/k(T) (and so E2/k(T) is not H-parametric
省10

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