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algebraic number theory - Ramification in a tower of extensions . . . 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
Ramification in cyclotomic fields - Mathematics Stack Exchange 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
Ramification in local fields - Mathematics Stack Exchange 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
Can someone explain tame and wild ramification in cubic integer rings? From my slow study of quadratic integer rings, it seems that there is only one "level" of ramification in those, so no one bothers to say if the ramification is "tame" or "wild," but I have seen those terms in regards to cubic algebraic integers To try to understand this, I thought I'd look at $\mathbb{Z}[\root 3 \of {12}]$
Ramification divisor and Hurwitz formula of higher dimensional varieties Notice that in this case, one can define the ramification index in just the same way Now the proof of Proposition 2 3, frankly, does not change at all You should also read Sándor Kovács answer , it really gave me a lot of perspective on the whole thing
Ramification index and residue class degree under completion I've got a problem in proving something written at page 111 of the book "Algebraic Number Theory" by A Fröhlich and M J Taylor This is the setting Let $\\mathfrak{o}$ be a Dedekind domain with
algebraic geometry - Why is $\infty$ a ramification point of a . . . But this might not actually be a point of ramification, since we haven't resolved the singularity yet If it resolves to one point, there is ramification If it resolves to two points, there is no ramification
what does it mean for a prime at infinity to ramify? $\begingroup$ 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