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Conjecture

Brumer-Stark Conjecture

Number Theory

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. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/

Facts
Progress Toward Resolution
In 2020 Dasgupta and Kakde proved the conjecture away from the prime 2, and in 2023 a full proof over Z was announced. 1
Classification
Resolution Status
Proven 1
Chronology
Resolved Year
2023 2
Prize Status
Prize Status (category)
No Prize Offered 1
Connections

In Branch

Algebraic Number Theory, Branches of Mathematics
Source Brumer-Stark conjecture (Wikipedia)
Sources
1. Brumer-Stark Conjecture (Wikipedia)
Wikimedia Foundation
  • Lead 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.
View the Source
2. The Brumer-Stark Conjecture over Z (arXiv preprint)
Abstract
Quote, Abstract
In this paper we give a complete proof of the Brumer-Stark conjecture over Z.
View the Source
Brumer-Stark conjecture (Wikipedia)
In Branch: Algebraic Number Theory, Lead sentenceView the Source
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