About: Leopoldt's conjecture

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In algebraic number theory, Leopoldt's conjecture, introduced by H.-W. Leopoldt , states that the p-adic regulator of a number field does not vanish. The p-adic regulator is an analogue of the usual regulator defined using p-adic logarithms instead of the usual logarithms, introduced by H.-W. Leopoldt.

Attributes	Values
rdf:type	yago:WikicatConjectures yago:Abstraction100002137 yago:Cognition100023271 yago:Concept105835747 yago:Content105809192 yago:Hypothesis105888929 yago:Idea105833840 yago:PsychologicalFeature100023100 yago:Speculation105891783
rdfs:label	Conjecture de Leopoldt (fr) Leopoldt's conjecture (en)
rdfs:comment	En théorie algébrique des nombres, la conjecture de Leopoldt, du nom du mathématicien Heinrich-Wolfgang Leopoldt, qui l'a formulée en 1962 dans un article paru au Journal für die reine und angewandte Mathematik, est un énoncé central, à la fois par le nombre de ses formulations équivalentes, touchant aux divers objets de la théorie, et par la richesse de ses conséquences. Il n'est actuellement démontré que pour le cas des extensions abéliennes du corps des nombres rationnels, par des méthodes relevant de l'étude de l'indépendance des nombres algébriques, à la suite de travaux d'Ax et Brumer, et pour certaines extensions de corps quadratiques imaginaires. (fr) In algebraic number theory, Leopoldt's conjecture, introduced by H.-W. Leopoldt , states that the p-adic regulator of a number field does not vanish. The p-adic regulator is an analogue of the usual regulator defined using p-adic logarithms instead of the usual logarithms, introduced by H.-W. Leopoldt. (en)
dcterms:subject	Conjectures Algebraic number theory Unsolved problems in number theory
Wikipage page ID	21829200 (xsd:integer)
Wikipage revision ID	1081994418 (xsd:integer)
Link from a Wikipage to another Wikipage	Quadratic field Totally real field Algebraic number field Regulator (mathematics) Dedekind zeta function Index of a subgroup Inventiones Mathematicae Conjectures Mathematika Algebraic number theory Number field Baker's theorem Prime number Abelian extension Abelian group Algebraic number theory Unsolved problems in number theory Diagonal embedding P-adic logarithm P-adic regulator Journal für die reine und angewandte Mathematik
Link from a Wikipage to an external page	http://projecteuclid.org/euclid.ijm/1256059299 http://resolver.sub.uni-goettingen.de/purl%3FGDZPPN002179482
sameAs	Leopoldt's conjecture Leopoldt's conjecture Leopoldt's conjecture Leopoldt's conjecture Leopoldt's conjecture
dbp:wikiPageUsesTemplate	dbt:As_of dbt:Citation dbt:Harvtxt dbt:Harvs dbt:Eom dbt:Neukirch_et_al._CNF
authorlink	Preda Mihăilescu (en) Heinrich-Wolfgang Leopoldt (en)
first	M. (en) H.-W. (en)
id	l/l110120 (en)
last	Kolster (en) Mihăilescu (en) Leopoldt (en)
year	1962 (xsd:integer) 1975 (xsd:integer) 2009 (xsd:integer) 2011 (xsd:integer)
has abstract	In algebraic number theory, Leopoldt's conjecture, introduced by H.-W. Leopoldt , states that the p-adic regulator of a number field does not vanish. The p-adic regulator is an analogue of the usual regulator defined using p-adic logarithms instead of the usual logarithms, introduced by H.-W. Leopoldt. Leopoldt proposed a definition of a p-adic regulator Rp attached to K and a prime number p. The definition of Rp uses an appropriate determinant with entries the p-adic logarithm of a generating set of units of K (up to torsion), in the manner of the usual regulator. The conjecture, which for general K is still open as of 2009, then comes out as the statement that Rp is not zero. (en) En théorie algébrique des nombres, la conjecture de Leopoldt, du nom du mathématicien Heinrich-Wolfgang Leopoldt, qui l'a formulée en 1962 dans un article paru au Journal für die reine und angewandte Mathematik, est un énoncé central, à la fois par le nombre de ses formulations équivalentes, touchant aux divers objets de la théorie, et par la richesse de ses conséquences. Il n'est actuellement démontré que pour le cas des extensions abéliennes du corps des nombres rationnels, par des méthodes relevant de l'étude de l'indépendance des nombres algébriques, à la suite de travaux d'Ax et Brumer, et pour certaines extensions de corps quadratiques imaginaires. (fr)
prov:wasDerivedFrom	wikipedia-en:Leopoldt's_conjecture?oldid=1081994418&ns=0
page length (characters) of wiki page	5113 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Leopoldt's_conjecture
is Link from a Wikipage to another Wikipage of	List of conjectures Heinrich-Wolfgang Leopoldt Jack Thorne (mathematician) James Ax Baker's theorem Dirichlet's unit theorem Greenberg's conjectures List of unsolved problems in mathematics Leopoldt conjecture
is Wikipage redirect of	Leopoldt conjecture
is foaf:primaryTopic of	wikipedia-en:Leopoldt's_conjecture

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