Category
page 1Theorems in algebraic number theory
Kronecker–Weber theorem
theorem
Ostrowski's theorem
on all absolute values of rational numbers
Dirichlet's unit theorem
theorem
Mordell–Weil theorem
theorem
Hilbert's Theorem 90
theorem
Chebotarev's density theorem
theorem
Hasse's theorem on elliptic curves
Stark–Heegner theorem
states precisely which quadratic imaginary number fields admit unique factorisation
Herbrand–Ribet theorem
theorem
principal ideal theorem
the theorem that extending ideals gives a mapping on the class group of an algebraic number field to the class group of its Hilbert class field, which sends all ideal classes to the class of a principal ideal
Albert–Brauer–Hasse–Noether theorem
central simple algebras over algebraic number fields that split over completions are matrix algebras