Algebraic Number Theory

The proof's method of identification of a deformation ring with a Hecke algebra (now referred to as an R=T theorem) to prove modularity lifting theorems has been an influential development in algebraic number theory.

Artin-Verdier duality is a duality theorem for constructible abelian sheaves over the spectrum of a ring of algebraic numbers

Takagi proved a conjecture on abelian extensions of imaginary number fields made by Kronecker

In algebraic number theory, a reflection theorem or Spiegelungssatz (German for reflection theorem - see Spiegel and Satz) is one of a collection of theorems linking the sizes of different ideal class groups (or ray class groups), or the sizes of different isotypic components of a class group.

In algebraic number theory, a Gauss sum or Gaussian sum is a particular kind of finite sum of roots of unity, typically G ( χ ) :=

In algebraic number theory, Leopoldt's conjecture, introduced by Heinrich-Wolfgang Leopoldt, states that the p-adic regulator of a

In algebraic number theory, the prime ideal theorem is the number field generalization of the prime number theorem.

ideal theorem of class field theory, a branch of algebraic number theory, says that extending ideals gives a mapping on the class

algebraic number theory

algebraic number theory

published more than 300 research papers on algebraic number theory

working in algebraic number theory and algebraic geometry

who introduced the Grunwald-Wang theorem

In mathematics, the Brauer-Siegel theorem, named after Richard Brauer and Carl Ludwig Siegel, is an asymptotic result on the behaviour of algebraic number fields, obtained by Richard Brauer and Carl Ludwig Siegel.

Sequences satisfying Gauss congruence naturally occur in the study of topological dynamics, algebraic number theory and combinatorics.

In mathematics, the Hilbert-Speiser theorem is a result on cyclotomic fields, characterising those with a normal integral

In class field theory, the Takagi existence theorem states that for

In mathematics, the discriminant of an algebraic number field is a numerical invariant that, loosely speaking

mathematics, the Herbrand-Ribet theorem is a result on the class group of certain number fields. It is a strengthening of Ernst Kummer's theorem

Jean-Pierre Serre is a French mathematician who has made important contributions to algebraic topology, algebraic geometry, and algebraic number theory.

Heinrich-Wolfgang Leopoldt was a German mathematician who worked in algebraic number theory.