Category
page 1Class field theory
class field theory
subarea of number theory
Iwasawa theory
study of objects of arithmetic interest over infinite towers of number fields
abelian extension
field extension whose Galois group is abelian
Kronecker–Weber theorem
theorem
Artin L-function
Type of Dirichlet series
complex multiplication
theory in mathematics
Galois cohomology
Group comohology of Galois modules
Hilbert symbol
Function used in local class field theory related to reciprocity laws
Hilbert class field
maximal abelian unramified extension of a number field
Artin reciprocity law
theorem
Langlands dual
group controlling representation theory
Weil group
concept in class field theory
Albert–Brauer–Hasse–Noether theorem
central simple algebras over algebraic number fields that split over completions are matrix algebras