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.

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All labels observed (5)

Label	Occurrences
Lubin–Tate theory	3
Lubin–Tate character	1
Lubin–Tate extension	1
Lubin–Tate formal groups canonical	1
Lubin–Tate formal groups (by analogy in local uniformization)	1

How this entity was disambiguated

This entity first appeared as the object of triple T10973517 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.

NED1 Entity disambiguation (via context triple) gpt-5-mini-2025-08-07

Target entity: Lubin–Tate formal groups
Context triple: [John Tate, notableWork, Lubin–Tate formal groups]

A. Drinfeld modules
Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
B. Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
C. Shafarevich group of a torus
The Shafarevich group of a torus is an arithmetic invariant measuring the failure of local-global principles for principal homogeneous spaces under an algebraic torus over a global field.
D. Furtwängler’s theorem in class field theory
Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
E. Iwasawa theory
Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
F. None of above. chosen
G. Unsure - the case is ambiguous/there is not enough information to decide.

NED2 Entity disambiguation (via description) gpt-5-mini-2025-08-07

Target entity: Lubin–Tate formal groups
Target entity description: 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.

A. Drinfeld modules
Drinfeld modules are algebraic structures that generalize elliptic curves to the setting of function fields, playing a central role in modern arithmetic geometry and the theory of automorphic forms.
B. Hasse–Arf theorem
The Hasse–Arf theorem is a fundamental result in algebraic number theory that precisely characterizes the jumps in the ramification filtration of abelian extensions of local fields, showing they occur at integer values.
C. Shafarevich group of a torus
The Shafarevich group of a torus is an arithmetic invariant measuring the failure of local-global principles for principal homogeneous spaces under an algebraic torus over a global field.
D. Furtwängler’s theorem in class field theory
Furtwängler’s theorem in class field theory is a fundamental result in algebraic number theory that refines the principal ideal theorem by describing how ideal classes capitulate (become principal) in certain abelian extensions of number fields.
E. Iwasawa theory
Iwasawa theory is a branch of number theory that studies the growth of arithmetic invariants in infinite towers of number fields, particularly using p-adic methods.
F. None of above. chosen

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 ⓘ linked to: Lubin–Tate formal groups local class field theory for finite extensions of Q_p ⓘ
associatedWith	Galois representations ⓘ Lubin–Tate character ⓘ linked to: Lubin–Tate formal groups Lubin–Tate extension ⓘ linked to: Lubin–Tate formal groups 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 ⓘ
generalizationOf	formal multiplicative group over Q_p ⓘ
givesRiseTo	Lubin–Tate tower ⓘ 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 ⓘ Jonathan Lubin ⓘ
parameterizedBy	choice of uniformizer of the local field ⓘ
relatedTo	Drinfeld modules ⓘ Honda formal groups ⓘ formal additive group ⓘ formal multiplicative group ⓘ local Langlands correspondence ⓘ 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 ⓘ

How these facts were elicited