Galois module information

In mathematics, a Galois module is a G-module, with G being the Galois group of some extension of fields. The term Galois representation is frequently...

theory. More generally one can define the Selmer group of a finite Galois module M (such as the kernel of an isogeny) as the elements of H1(GK,M) that...

arithmetic interest over infinite towers of number fields. It began as a Galois module theory of ideal class groups, initiated by Kenkichi Iwasawa (1959) (岩澤...

can never form a Z-module basis of Z[i] because 1 cannot be an integer combination. The reasons are studied in depth in Galois module theory. The regular...

normal integral basis is part of Galois module theory. Let F ⊂ K {\displaystyle F\subset K} be a Galois extension with Galois group G {\displaystyle G} . The...

mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups...

situations, the Galois group acts on other mathematical objects, for example a group. Such a group is then also referred to as a Galois module. This enables...

G are an abelian group. The p-adic Tate module Tp(G) of G is a Galois representation (of the absolute Galois group, GK, of K). Classical results on abelian...

In Galois cohomology, local Tate duality (or simply local duality) is a duality for Galois modules for the absolute Galois group of a non-archimedean...

of the Milnor K-group of a field k with the Galois cohomology of k with coefficients in the Galois module of ℓth roots of unity. The point of the conjecture...

action of the absolute Galois group of K. Given a finite separable field extension L/K and a torus T over L, we have a Galois module isomorphism X ∙ ( R...

of extensions is known better when L/K is Galois. Let (K, v) be a valued field and let L be a finite Galois extension of K. Let Sv be the set of equivalence...

universal deformation rings and Hecke algebras. Deformation (mathematics) Galois module Cornell, Gary; Silverman, Joseph H.; Stevens, Glenn, eds. (1997), Modular...

Frobenius reciprocity. Galois A Galois module is a module over the group ring of a Galois group. generating set A subset of a module is called a generating...

algebraic group Global field Hasse principle Hasse–Minkowski theorem Galois module Galois cohomology Brauer group Class field theory Abelian extension Kronecker–Weber...

field theory. Unlike the classical case, Milnor K-groups do not satisfy Galois module descent if n > 1 {\displaystyle n>1} . General higher-dimensional local...

In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements. As with any...

created by Kenkichi Iwasawa, Iwasawa theory was originally developed as a Galois module theory of ideal class groups. The main conjecture of Iwasawa theory...

this goal when K is an abelian extension of Q (that is, a Galois extension with abelian Galois group). Unique factorization fails if and only if there are...