Embedding problems over large fields
Embedding problems over large fields
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大范围内的嵌入问题
DOI：
10.2307/2118581
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发表时间：
1996
影响因子：
4.9
通讯作者：
F. Pop
中科院分区：
文献类型：
--
作者：
F. Pop
在本文中，我们研究了一大类域的伽罗瓦理论性质，这类域包括所有满足泛局部-全局原理的域，该原理是关于簇上有理点的存在性的。作为应用，我们给出了一个长期存在的猜想的肯定答案，该猜想起源于Roquette的一个未发表的笔记，并断言可数的希尔伯特PAC域的绝对Galois群是profinite free的;见[F-J，问题24.41]。其次，我们给出了Shafarevich猜想的新证据，该猜想断言Qab的绝对Galois群是profinite free的。最后，我们在这里开发的理论的最有趣的应用之一是在伽罗瓦结构的全EG-adic数的洞察力。
In this paper we study Galois theoretic properties of a large class of fields, a class which includes all fields satisfying a universal local-global principle for the existence of rational points on varieties. As applications, we give a positive answer to a long standing conjecture which originates in an unpublished note of Roquette, and asserts that the absolute Galois group of a countable, hilbertian, PAC field is profinite free; see [F-J, Problem 24.41]. Secondly, we give new evidence for the conjecture of Shafarevich which asserts that the absolute Galois group of Qab is profinite free. Finally, one of the most interesting applications of the theory we develop here is the insight in the Galois structure of the totally EG-adic numbers.