Theorem

Chebotarev Density Theorem

Number Theory

Describes the statistical distribution of Frobenius elements, and hence of prime splitting behavior, across the Galois group of a number field extension. It generalizes Dirichlet's theorem on primes in arithmetic progressions and underlies much of modern algebraic number theory.

Facts

Statement

For a finite Galois extension of a number field with Galois group G, the primes that are unramified and whose Frobenius conjugacy class lies in a fixed conjugation-stable subset of G have density equal to the proportion that subset occupies within G. 1

Proof Year

1922 1

Classification

Statement Form

Identity or Equation 1

Connections

Source Chebotarev Density Theorem (Wikipedia)

Sources

1. Chebotarev Density Theorem (Wikipedia)

Wikimedia Foundation

Important consequences section, first sentence
The Chebotarev density theorem reduces the problem of classifying Galois extensions of a number field to that of describing the splitting of primes in extensions.
History and motivation section, closing sentence
The general statement was proved by Nikolai Grigoryevich Chebotaryov in 1922.
Proved By: Nikolai Chebotaryov, Lead
It was proved by Chebotarev in his thesis in 1922.

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Chebotarev Density Theorem

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