Furtwängler’s theorem in class field theory
E713105
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.
Statements (27)
| Predicate | Object |
|---|---|
| instanceOf |
result in class field theory
ⓘ
theorem in algebraic number theory ⓘ |
| appliesTo |
Hilbert class fields
NERFINISHED
ⓘ
number fields ⓘ |
| concerns |
abelian extensions of number fields
ⓘ
capitulation of ideal classes ⓘ ideal class groups ⓘ |
| context |
Galois theory of number fields
ⓘ
maximal unramified abelian extensions ⓘ |
| describes | conditions under which ideal classes become principal in extensions ⓘ |
| field |
algebraic number theory
ⓘ
class field theory ⓘ |
| hasImportance |
fundamental in the study of capitulation in class field theory
ⓘ
refines understanding of principalization of ideals ⓘ |
| implies | capitulation of certain ideal classes in the Hilbert class field ⓘ |
| namedAfter | Philipp Furtwängler NERFINISHED ⓘ |
| refines | principal ideal theorem NERFINISHED ⓘ |
| relatedTo |
Hilbert class field
NERFINISHED
ⓘ
class field theory reciprocity laws ⓘ ideal class capitulation ⓘ principal ideal theorem ⓘ |
| studiedIn |
advanced texts on algebraic number theory
ⓘ
treatises on global class field theory ⓘ |
| usesConcept |
Artin reciprocity
NERFINISHED
ⓘ
class field ⓘ ideal class group ⓘ norm map on ideal class groups ⓘ |
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.