the ramification groups are a filtration of the Galois group of a local field extension, which gives detailed information on the ramification phenomena...

Look up ramification in Wiktionary, the free dictionary. Ramification may refer to: Ramification (mathematics), a geometric term used for 'branching out'...

In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing...

detailed analysis can be carried out with the aid of tools such as ramification groups. In this article, a local field is non-archimedean and has finite...

(first) ramification group. If K is a local or global field, the theory of class formations attaches to K its Weil group WK, a continuous group homomorphism...

v_{L}} . Let L / K {\displaystyle L/K} have Galois group G and define the s-th ramification group of L / K {\displaystyle L/K} for any real s ≥ −1 by...

Hensel's lemma, Galois extensions of local fields, ramification groups filtrations of Galois groups of local fields, the behavior of the norm map on local...

extension of local or global fields provides a quantitative measure of the ramification in the extension. The definition of the conductor is related to the Artin...

graduate-level algebraic number theory text covering local fields, ramification, group cohomology, and local class field theory. The book's end goal is...

0}{\frac {g_{i}}{g_{0}}}(\chi (1)-\chi (G_{i}))} where Gi is the i-th ramification group (in lower numbering), of order gi, and χ(Gi) is the average value...

restriction of w to K is v. The set of all such extensions is studied in the ramification theory of valuations. Let L/K be a finite extension and let w be an extension...

with a symmetry group of transformations G {\displaystyle G} . Since the symmetry group has stabilizers at the points of the ramification locus, branched...

number field K, with respect to the field trace. It then encodes the ramification data for prime ideals of the ring of integers. It was introduced by Richard...

normal form of a formula, dual to Skolemization Herbrand's theorem on ramification groups Rollo Davidson (1944–1970) – another mathematician who died in a...

multiplicative group of a field and the character group of the absolute Galois group of the algebraic closure of the field is proved. Ramification theory for...

(2005), "Completing Artin's braid group on infinitely many strands", Journal of Knot Theory and Its Ramifications, 14 (8): 979–991, arXiv:math/0201303...

f(z_{0})} is a positive integer called the ramification index of z 0 {\displaystyle z_{0}} . If the ramification index is greater than 1, then z 0 {\displaystyle...

"Semiabelian Groups and the Inverse Galois Problem". Courant Institute of Mathematical Sciences. De Witt, Meghan (2014). "Minimal ramification and the inverse...

{\displaystyle k} ramification points p i ∈ X / G {\displaystyle p_{i}\in X/G} for the quotient map X → X / G {\displaystyle X\to X/G} . The ramification index e...

Quadratic reciprocity Ideal class group Dirichlet's unit theorem Discriminant of an algebraic number field Ramification (mathematics) Root of unity Gaussian...

is an extension generated by radicals of elements. ramification group A ramification group is a group of automorphisms of a ring R fixing some given prime...

Ramifications is a composition for strings by Hungarian composer György Ligeti. It was finished in 1968 and premiered in 1969. The composition is dedicated...

1007/s002080100262, S2CID 29899627 Achinger, Piotr (November 2017). "Wild ramification and K(pi, 1) spaces". Inventiones Mathematicae. 210 (2): 453–499. arXiv:1701...

of early Islam, with all the political, religious and eschatological ramifications that this would imply. Abu Abdullah al-Muhajir, an Egyptian Jihadist...

things are: ramification groups and the Nottingham group", in du Sautoy, Marcus; Segal, Dan; Shalev, Aner (eds.), New horizons in pro-p groups, Progress...

associated exponents, which encode the ramification in the field extensions generated by the points of finite order in the group law of the elliptic curve. The...

adjoining a root of x3 - x - 1, which has discriminant -23. To see why ramification at the archimedean primes must be taken into account, consider the real...

is closely associated with covering maps and their degeneration into ramification; the aspect giving rise to monodromy phenomena is that certain functions...

the Riemann sphere, with ramification locus at the set of vertices of the regular inscribed octahedron. Its automorphism group includes the hyperelliptic...

Wesley enlist the help of the DEA, but they are bound by the political ramifications of the case. Nolan, Tim and Harper enlist Max, who gives them a helicopter...