关于一组名词的亲p-扩张局部最大分圆
Sur la pro-p-extension localement cyclotomique maximale d'un corps de nombres
摘要：
设p是素数，F是数域.考虑F的分圆Z_p扩张的极大非分歧p-分解pro-p-扩张的分圆Z_p扩张上的伽罗瓦群G. G是否是自由亲p的问题已经被许多作者提出。在这篇文章中，我们强调了G的自由度和一些局部化核的伽罗瓦下降之间的联系。然后给出了G不是自由pro-p-群的充分条件。
英文摘要：
Let p be a prime number and F be a number field. We consider the Galois group G over the cyclotomic Z_p extension of F of the maximal unramified, p-decomposed, pro-p-extension of the cyclotomic Z_p extension of F. The question whether G is free pro-p was already asked by many authors. In this article, we highlight a link between the freeness of G and the Galois descent for some localisation kernels. Then we give explicit criterions to show that G is not a free pro-p-group.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
