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The Brumer–Stark conjecture is a conjecture in algebraic number theory giving a rough generalization of both the analytic class number formula for Dedekind zeta functions, and also of Stickelberger's theorem about the factorization of Gauss sums. It is named after and Harold Stark. It arises as a special case (abelian and first-order) of Stark's conjecture, when the place that splits completely in the extension is finite. There are very few cases where the conjecture is known to be valid. Its importance arises, for instance, from its connection with Hilbert's twelfth problem.

Attributes	Values
rdf:type	yago:WikicatConjectures yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:PsychologicalFeature100023100 yago:Speculation105891783
rdfs:label	Brumer–Stark conjecture (en) Conjecture de Brumer-Stark (fr)
rdfs:comment	The Brumer–Stark conjecture is a conjecture in algebraic number theory giving a rough generalization of both the analytic class number formula for Dedekind zeta functions, and also of Stickelberger's theorem about the factorization of Gauss sums. It is named after and Harold Stark. It arises as a special case (abelian and first-order) of Stark's conjecture, when the place that splits completely in the extension is finite. There are very few cases where the conjecture is known to be valid. Its importance arises, for instance, from its connection with Hilbert's twelfth problem. (en) La conjecture de Brumer-Stark est une conjecture en théorie algébrique des nombres donnant une généralisation à la fois de la formule analytique des nombres de classe pour les fonctions zêta de Dedekind et aussi du théorème de Stickelberger sur la factorisation des sommes de Gauss. Elle porte les noms d'Armand Brumer et Harold Stark. (fr)
dcterms:subject	Conjectures Zeta and L-functions Algebraic number theory Unsolved problems in number theory
Wikipage page ID	20510092 (xsd:integer)
Wikipage revision ID	1121390651 (xsd:integer)
Link from a Wikipage to another Wikipage	Prime ideal Quadratic extension Samit Dasgupta Module (mathematics) C. L. Siegel Euler factor Annals of Mathematics John Tate (mathematician) Dedekind zeta function Conjectures Complex number Conjecture Equivariant L-function Roots of unity Annihilator (ring theory) Stickelberger's theorem Ideal class group G-module Galois group Algebraic number theory Zeta and L-functions Factorization Fractional ideal Global field Hilbert's twelfth problem Ramification theory of valuations Harold Stark Abelian extension Algebraic number theory Unsolved problems in number theory Ken Ribet Artin L-function Pierre Deligne Group ring Takuro Shintani Archimedean place Analytic class number formula Function field analogy Gauss sums Place (number theory) Completely split Stark's conjecture dbr:Armand_Brumer dbr:Biquadratic_extension dbr:Pierrette_Cassou-Noguès dbr:Daniel_Barsky
sameAs	Brumer–Stark conjecture Brumer–Stark conjecture Brumer–Stark conjecture Brumer–Stark conjecture
dbp:wikiPageUsesTemplate	dbt:! dbt:= dbt:Math dbt:Reflist
has abstract	The Brumer–Stark conjecture is a conjecture in algebraic number theory giving a rough generalization of both the analytic class number formula for Dedekind zeta functions, and also of Stickelberger's theorem about the factorization of Gauss sums. It is named after and Harold Stark. It arises as a special case (abelian and first-order) of Stark's conjecture, when the place that splits completely in the extension is finite. There are very few cases where the conjecture is known to be valid. Its importance arises, for instance, from its connection with Hilbert's twelfth problem. (en) La conjecture de Brumer-Stark est une conjecture en théorie algébrique des nombres donnant une généralisation à la fois de la formule analytique des nombres de classe pour les fonctions zêta de Dedekind et aussi du théorème de Stickelberger sur la factorisation des sommes de Gauss. Elle porte les noms d'Armand Brumer et Harold Stark. Elle apparaît comme un cas particulier (abélien et du premier ordre) de la (en), lorsque la place qui se scinde dans l'extension est finie. Il y a très peu de cas où la conjecture est connue comme vraie. Son importance découle, par exemple, de sa connexion avec le douzième problème de Hilbert. (fr)
gold:hypernym	Conjecture
prov:wasDerivedFrom	wikipedia-en:Brumer–Stark_conjecture?oldid=1121390651&ns=0
page length (characters) of wiki page	5786 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Brumer–Stark_conjecture
is Link from a Wikipage to another Wikipage of	List of conjectures Special values of L-functions Cristian Dumitru Popescu Brumer Brumer-Stark conjecture Equivariant L-function Harold Stark Pierre Deligne List of unsolved problems in mathematics
is Wikipage redirect of	Brumer-Stark conjecture
is Wikipage disambiguates of	Brumer
is foaf:primaryTopic of	wikipedia-en:Brumer–Stark_conjecture

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