تقرير
Twisted Class Field Theory
| العنوان: | Twisted Class Field Theory |
|---|---|
| المؤلفون: | Yoon, Seok Ho Jack |
| سنة النشر: | 2015 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Number Theory |
| الوصف: | Neukirch has developed explicit and axiomatic class field theory, which applies to both local and global fields. One of the key ingredients in his theory is a $\hat{\mathbb{Z}}$-extension of the base field, and in the case of $\mathbb{Q}_p$, he uses the maximal unramified extension. However $\mathbb{Q}_p$ has another $\hat{\mathbb{Z}}$-extension, which we shall denote by $\hat{\mathbb{Q}}_p$. Thus, it is natural to ask if we could verify all the axioms required by taking $\hat{\mathbb{Q}}_p$ as the central object instead. We prove this is possible and the two reciprocity maps induced from the two distinct $\hat{\mathbb{Z}}$-extensions are the same. Comment: Crucial error. Found a fundamental mistake which would make the statement of the paper. In fact there exists no such henselian valuation which would make Neukirch class field theory work for the $\hat{\mathbb{Z}}$ extension \hat{\mathbb{Q}}_p$ |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/1506.05365 |
| رقم الأكسشن: | edsarx.1506.05365 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |