The Brumer-Stark conjecture, in algebraic number theory, is named after Armand Brumer and Harold Stark and gives a rough generalization of both the analytic class number formula for Dedekind zeta functions and Stickelberger's theorem on the factorization of Gauss sums. It arises as a special abelian, first-order case of Stark's conjecture, and there are very few cases where it is known to be valid; its importance arises in part from its connection to Hilbert's twelfth problem.
Facts
Progress Toward ResolutionIn 2020 Dasgupta and Kakde proved the conjecture away from the prime 2, and in 2023 a full proof over Z was announced. 1 Difficulty Hint Classification
Resolution Status Chronology
Resolved Year Prize Status
Prize Status (category) Connections
In Branch
Source Brumer-Stark conjecture (Wikipedia)
Posed By
Source Brumer-Stark Conjecture (Wikipedia)
Sources
1. Brumer-Stark Conjecture (Wikipedia)
Wikimedia FoundationLead section
There are very few cases where the conjecture is known to be valid.
Progress section, Dasgupta and Kakde
In 2020, Dasgupta and Kakde proved the Brumer-Stark conjecture away from the prime 2.
Progress section, 2023 full proof sentence
In 2023, a full proof of the conjecture over Z has been announced.
Posed By: John Tate, Lead
The conjecture was first stated in published form by John Tate
View the Source 2. The Brumer-Stark Conjecture over Z (arXiv preprint)
AbstractQuote, Abstract
In this paper we give a complete proof of the Brumer-Stark conjecture over Z.
3. Brumer-Stark conjecture (Wikipedia)
Lead section
a rough generalization of both the analytic class number formula for Dedekind zeta functions
- In Branch: Algebraic Number Theory, Lead sentence
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