Mild pro-p-groups and p-extensions of number fields with restricted ramification

具有有限分支的数域的轻度亲 p 群和 p 扩展

• 批准号: 4344-2006
• 负责人: Labute, John
• 金额: $ 0.66万
• 依托单位: McGill University
• 依托单位国家: 加拿大
• 项目类别: Discovery Grants Program - Individual
• 财政年份: 2007
• 资助国家: 加拿大
• 起止时间: 2007-01-01 至 2008-12-31
• 项目状态: 已结题
• 来源: https://www.nserc-crsng.gc.ca/ase-oro/Details-Detailles_eng.asp?id=364823
• 关键词: Mild; pro; groups; extensions; number

The Galois group of the maximal p-extension of a number field with restricted tame ramification is one of the most mysterious objects in number theory. Little was known about this group until our breakthrough result last year in the case of the rational field which showed that this group was in a large proportional of cases a mild group and hence of cohomological dimension 2. We propose to continue this research in the hope of extending our results by finding an algorithm for mildness. We have obtained such an algorithm in the 4-generator case. We also want to extend our results to other number fields such as quadratic imaginary number fields.

具有限制驯服分支的数域的极大p-扩张的伽罗瓦群是数论中最神秘的对象之一。很少有人知道这个群体，直到我们的突破性结果，去年的情况下，合理的领域，这表明这一组是在很大比例的情况下，一个温和的群体，因此上同调维数2。我们建议继续这项研究，希望通过找到一种温和的算法来扩展我们的结果。我们在4生成元情形下得到了这样一个算法。我们也希望将我们的结果推广到其他数域，如二次虚数域。