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

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...

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...

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

(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...

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...

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

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...

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...

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...

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...

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...

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

(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...

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

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

{\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...

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

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...

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...

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

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

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

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

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

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

is the ramification index e ( P α , i ) {\displaystyle e(P_{\alpha ,i})} at each of the ( m , r α ) {\displaystyle (m,r_{\alpha })} ramification points...

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...

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...