Neukirch: Algebraic Number Theory

E459564
algebraic number theory textbook mathematics book textbook

"Neukirch: Algebraic Number Theory" is a widely respected graduate-level textbook that provides a rigorous, modern introduction to algebraic number theory, including class field theory and foundational results such as the Kronecker–Weber theorem.

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All labels observed (2)

Label Occurrences
Algebraic Number Theory 1
Neukirch: Algebraic Number Theory canonical 1

Statements (47)

Predicate Object
instanceOf algebraic number theory textbook ⓘ
mathematics book ⓘ
textbook ⓘ
author Jürgen Neukirch NERFINISHED ⓘ
countryOfPublication Germany NERFINISHED ⓘ
field algebraic number theory ⓘ
hasCompanionVolume Neukirch: Cohomology of Number Fields NERFINISHED ⓘ
language English ⓘ
German ⓘ
level graduate ⓘ
notableFor idele-theoretic approach to class field theory ⓘ
rigorous and modern treatment of class field theory ⓘ
systematic use of valuations and completions ⓘ
originalPublicationYear 1992 ⓘ
prerequisite Galois theory ⓘ
abstract algebra ⓘ
commutative algebra ⓘ
publicationYear 1999 ⓘ
publisher Springer-Verlag NERFINISHED ⓘ
series Grundlehren der mathematischen Wissenschaften NERFINISHED ⓘ
Springer Monographs in Mathematics NERFINISHED ⓘ
subject Artin reciprocity NERFINISHED ⓘ
Dedekind domains NERFINISHED ⓘ
Dirichlet unit theorem NERFINISHED ⓘ
Galois theory of number fields ⓘ
Kronecker–Weber theorem NERFINISHED ⓘ
L-functions ⓘ
Minkowski theory ⓘ
adeles ⓘ
cohomological methods in number theory ⓘ
discriminants ⓘ
global class field theory ⓘ
ideal class groups ⓘ
ideles ⓘ
local class field theory ⓘ
local fields ⓘ
local-global principles ⓘ
number fields ⓘ
ramification theory ⓘ
units in number fields ⓘ
valuations ⓘ
zeta functions of number fields ⓘ
translatedFrom Neukirch: Algebraische Zahlentheorie NERFINISHED ⓘ
translator Kay Wingberg NERFINISHED ⓘ
Norbert Schappacher NERFINISHED ⓘ
usedAs graduate textbook ⓘ
usedIn graduate courses in algebraic number theory ⓘ

Referenced by (2)

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

Kronecker–Weber theorem → standardReference → Neukirch: Algebraic Number Theory ⓘ
Jürgen Neukirch → notableWork → Neukirch: Algebraic Number Theory ⓘ
this entity surface form: Algebraic Number Theory