unramified ideal
11Étale morphism — In algebraic geometry, a field of mathematics, an étale morphism (pronunciation IPA|) is an algebraic analogue of the notion of a local isomorphism in the complex analytic topology. They satisfy the hypotheses of the implicit function theorem,… …
12Takagi existence theorem — In class field theory, the Takagi existence theorem states that for any number field K there is a one to one inclusion reversing correspondence between the finite abelian extensions of K (in a fixed algebraic closure of K ) and the generalized… …
13Ramification — In mathematics, ramification is a geometric term used for branching out , in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign. It is also used from the opposite perspective (branches… …
14Henselian ring — In mathematics, a Henselian ring (or Hensel ring) is a local ring in which Hensel s lemma holds. They were defined by harvtxt|Azumaya|1951, who named them after Kurt Hensel. Some standard references for Hensel rings are… …
15Artin L-function — In mathematics, an Artin L function is a type of Dirichlet series associated to a linear representation ρ of a Galois group G . These functions were introduced in the 1923 by Emil Artin, in connection with his research into class field theory.… …
16Cotangent complex — In mathematics the cotangent complex is a roughly a universal linearization of a morphism of geometric or algebraic objects. Cotangent complexes were originally defined in special cases by a number of authors. Luc Illusie, Daniel Quillen, and M.… …
17Teorema de Herbrand-Ribet — En matemáticas, el Teorema de Herbrand–Ribet es un resultado del número de clase de ciertos campos de números. Es un refuerzo del teorema de Kummer en el sentido que el número primo p divide el número de clase del campo ciclotómico de la p… …
18Serre's multiplicity conjectures — In mathematics, Serre s multiplicity conjectures are certain purely algebraic problems, in commutative algebra, motivated by the needs of algebraic geometry. Since André Weil s initial rigorous definition of intersection numbers, around 1949,… …
19Conductor (class field theory) — In algebraic number theory, the conductor of a finite abelian 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 map. Contents 1 Local… …
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