Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

2022年5月25日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

If a prime power divides $\mathfrak{m}$, then we can control ramification at that prime. There's a little more we can do. Sometimes a field can split over the real/complex numbers. We can control that by adding an additional, artificial term to $\mathfrak{m}$, making it a Modulus. We can then get Ray Class Fields of this modulus as well.

2014年11月29日 · So, the best place to start thinking about ramification, is in terms of maps of Riemann surfaces. While this may seem unrelated at first, bear through it, and I promise (hopefully!) it will make sense at the end.

2020年7月5日 · You mention a formula for the discriminant in tame ramification, what is this formula (a cursory search through my references hasn't revealed anything)? $\endgroup$ – Nico Commented Jul 5, 2020 at 19:11

2011年2月18日 · $\begingroup$ The above definition of ramification for real places is the usual one, justified e.g. by the ramification index 2 which appears in a complex valuation over a real one (see Joequinn's answer). However the same phenomenon could also be interpreted as the splitting of the real place under the complex one.

2021年1月21日 · Question: I know how to detect ramified or unramified fields in the case of number fields. But I have no feelings about how to do this for local fields. How should I find that $\\mathbb{Q}_p(\\sqrt[3...

2019年8月7日 · I'm studying from The Arithmetic of Elliptic Curves (Silverman) and I'm having a hard time understanding the intuition behind the $\\textit{ramification index}$ concept. In the book, we let $\\phi:...

2011年12月31日 · The higher ramification groups correspond to naturally arising groups of local units; namely, their image under the Artin map are precisely the higher powers of the local 1-units. In fact, historically more basic than the previous point is that the first very careful proofs of Kronecker-Weber (i.e., before class field theory existed) by Hilbert ...