Lubin–Tate formal groups
E896826
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.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Lubin–Tate formal groups canonical | 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
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 ⓘ |
How these facts were elicited
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Instruction
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Input
Subject: Lubin–Tate formal groups Description of subject: 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.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.