p-adic analytic groups
E581256
p-adic analytic groups are topological groups over the p-adic numbers that locally resemble finite-dimensional p-adic manifolds and admit a compatible analytic structure.
All labels observed (1)
| Label | Occurrences |
|---|---|
| p-adic analytic groups canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6282321 — 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: p-adic analytic groups Context triple: [Lie ring, isUsedIn, p-adic analytic groups]
-
A.
p-adic numbers
The p-adic numbers are a system of number fields that extend the rational numbers by measuring distance with respect to divisibility by a fixed prime p, playing a central role in modern number theory and arithmetic geometry.
-
B.
p-adic Hodge theory
p-adic Hodge theory is a branch of arithmetic geometry that studies p-adic Galois representations and their relationship to the cohomology of algebraic varieties over p-adic fields, using analogues of classical Hodge-theoretic structures.
-
C.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
-
D.
Adeles and Algebraic Groups
"Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
-
E.
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.
- 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: p-adic analytic groups Target entity description: p-adic analytic groups are topological groups over the p-adic numbers that locally resemble finite-dimensional p-adic manifolds and admit a compatible analytic structure.
-
A.
p-adic numbers
The p-adic numbers are a system of number fields that extend the rational numbers by measuring distance with respect to divisibility by a fixed prime p, playing a central role in modern number theory and arithmetic geometry.
-
B.
p-adic Hodge theory
p-adic Hodge theory is a branch of arithmetic geometry that studies p-adic Galois representations and their relationship to the cohomology of algebraic varieties over p-adic fields, using analogues of classical Hodge-theoretic structures.
-
C.
Algebraic Groups and Class Fields
"Algebraic Groups and Class Fields" is a influential mathematical monograph that develops the deep connections between algebraic group theory and class field theory within number theory and arithmetic geometry.
-
D.
Adeles and Algebraic Groups
"Adeles and Algebraic Groups" is a foundational mathematical work by André Weil that develops the theory of adeles and its deep connections with algebraic groups and number theory.
-
E.
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.
- F. None of above. chosen
Statements (50)
| Predicate | Object |
|---|---|
| instanceOf |
mathematical concept
ⓘ
p-adic Lie group ⓘ topological group theory concept ⓘ |
| admits | p-adic Lie algebra ⓘ |
| associatedWith | p-adic differential equations ⓘ |
| compatibilityCondition | group operations are analytic maps ⓘ |
| contrastWith |
complex Lie groups
ⓘ
real Lie groups ⓘ |
| definedOver |
Q_p
ⓘ
p-adic numbers ⓘ |
| dimension | finite ⓘ |
| field |
algebra
ⓘ
number theory ⓘ p-adic analysis ⓘ representation theory ⓘ |
| generalizes | analytic Lie groups over Q_p ⓘ |
| hasExample |
GL_n(Q_p)
ⓘ
SL_n(Q_p) ⓘ Z_p^n as an additive group ⓘ compact open subgroups of GL_n(Q_p) ⓘ p-adic points of a linear algebraic group over Q_p ⓘ |
| hasInvariantMeasure | Haar measure ⓘ |
| hasMorphisms | continuous analytic group homomorphisms ⓘ |
| hasNeighborhoodBase | p-adic analytic submanifolds ⓘ |
| hasOperation |
group inversion
ⓘ
group multiplication ⓘ |
| hasProperty |
Hausdorff
ⓘ
analytic in the p-adic sense ⓘ first countable ⓘ locally compact ⓘ locally homeomorphic to Q_p^n ⓘ paracompact ⓘ totally disconnected ⓘ |
| hasStructure |
analytic structure
ⓘ
p-adic manifold ⓘ topological group ⓘ |
| hasTangentObject | Lie algebra over Q_p ⓘ |
| localCoordinateModel | open subsets of Q_p^n ⓘ |
| locallyResembles | finite-dimensional p-adic manifold ⓘ |
| relatedConcept |
Lie group
ⓘ
p-adic Lie algebra ⓘ profinite group ⓘ rigid analytic space ⓘ |
| specialCaseOf | locally analytic groups over non-Archimedean fields ⓘ |
| studiedIn |
Iwasawa theory
ⓘ
p-adic representation theory ⓘ |
| typicalTopology | non-Archimedean ⓘ |
| usedIn |
automorphic forms
ⓘ
local Langlands correspondence ⓘ
linked to:
Weil–Deligne representations
non-Archimedean harmonic analysis ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: p-adic analytic groups Description of subject: p-adic analytic groups are topological groups over the p-adic numbers that locally resemble finite-dimensional p-adic manifolds and admit a compatible analytic structure.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.