May 25, 2022 · The prime p p is totally ramified in Kpr K p r with ramification index [Kpr: Q] = φ(pr) [K p r: Q] = φ (p r) and p p is unramified in Kn K n. In the composite field Km K m, the ramification index of p …

The ramification in intermediate fields is a slightly delicate (purely group theoretic) issue. First, assume without loss of generality that L/K L / K is Galois with Galois group G G, otherwise pass to the Galois …

Feb 18, 2011 · 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). …

By the Riemann-Hurwitz formula the degree of the ramification divisor is 4, hence ϕ ϕ can ramify in three possible ways: (a) two points of ramification index 3; (b) one point of ramification index 3 and two …

23 I am a beginner student of Algebraic Number Theory and I am starting to learn ramification theory (of global fields). My question asks for motivation for a definition I was given. Let K K be an algebraic …

Ramification index and inertia degree Ask Question Asked 15 years, 1 month ago Modified 15 years, 1 month ago

Apr 12, 2020 · Many of these references eventually mention "branch" or "ramification" in passing or loosely, as if assuming the reader knows about it. So my questions are: What are the definitions of …

Feb 11, 2021 · Ramification divisor and Hurwitz formula of higher dimensional varieties Ask Question Asked 12 years, 5 months ago Modified 4 years, 11 months ago

Let K K be a number field, n n be a positive integer and ζn ζ n a primitve nth n t h root of unity. How does one show that if a prime ideal p p of K K is ramified in K(ζn) K (ζ n) then n ∈ p n ∈ p ? (This is not …

Jul 6, 2012 · Ramification of primes Ask Question Asked 13 years, 6 months ago Modified 13 years, 6 months ago