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
StatementFor 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 Classification
Statement Form Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Sources
1. Chebotarev Density Theorem (Wikipedia)
Wikimedia FoundationImportant 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.
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