Lubin–Tate formal groups

E896826

formal group law mathematical object one-dimensional formal group law

Lubin–Tate formal groups are a class of one-dimensional formal group laws over local fields that play a central role in local class field theory by providing explicit descriptions of abelian extensions.

Try in SPARQL Jump to: Surface forms Statements Referenced by

All labels observed (1)

Label	Occurrences
Lubin–Tate formal groups canonical	1

Statements (48)

Predicate	Object
instanceOf	formal group law ⓘ mathematical object ⓘ one-dimensional formal group law ⓘ
actsOn	maximal ideal of the ring of integers of a local field ⓘ
appearsIn	Lubin–Tate theory NERFINISHED ⓘ local class field theory for finite extensions of Q_p ⓘ
associatedWith	Galois representations ⓘ Lubin–Tate character NERFINISHED ⓘ Lubin–Tate extension NERFINISHED ⓘ local reciprocity law ⓘ p-adic representations ⓘ uniformizer of a local field ⓘ
centralRoleIn	description of the Galois group of the maximal abelian extension of a local field ⓘ explicit construction of the local reciprocity isomorphism ⓘ
constructedFrom	chosen uniformizer of the local field ⓘ power series over the ring of integers of a local field ⓘ
definedOver	finite extensions of Q_p ⓘ local fields ⓘ non-archimedean local fields ⓘ
dimension	1 ⓘ
fieldOfStudy	algebraic number theory ⓘ local class field theory ⓘ number theory ⓘ p-adic Hodge theory NERFINISHED ⓘ
generalizationOf	formal multiplicative group over Q_p ⓘ
givesRiseTo	Lubin–Tate tower NERFINISHED ⓘ tower of totally ramified abelian extensions ⓘ
hasProperty	commutative ⓘ defined by a formal group law over the ring of integers of a local field ⓘ gives canonical formal module structure on maximal ideal of ring of integers ⓘ one-dimensional ⓘ
namedAfter	John Tate NERFINISHED ⓘ Jonathan Lubin NERFINISHED ⓘ
parameterizedBy	choice of uniformizer of the local field ⓘ
relatedTo	Drinfeld modules NERFINISHED ⓘ Honda formal groups ⓘ formal additive group ⓘ formal multiplicative group ⓘ local Langlands correspondence NERFINISHED ⓘ p-divisible groups ⓘ
usedFor	construction of Lubin–Tate extensions ⓘ construction of abelian extensions of local fields ⓘ description of the local reciprocity map ⓘ explicit description of the maximal abelian extension of a local field ⓘ explicit local class field theory ⓘ
usedIn	construction of local epsilon factors ⓘ construction of p-adic periods ⓘ
yearIntroduced	1965 ⓘ

Referenced by (1)

Full triples — surface form annotated when it differs from this entity's canonical label.

John Tate → notableWork → Lubin–Tate formal groups ⓘ