User:RobHar/Sandbox3
History[edit]
Basic notions[edit]
- Algebraic number fields
- Class groups
- Primes and places
- Unit groups
- Discriminant of an algebraic number field
- Conductor
- Localization
Branches of algebraic number theory[edit]
Major results[edit]
- Finiteness of the class number
- Dirichlet's unit theorem
- Kronecker–Weber theorem
- Artin reciprocity
- Class number formula
Open questions[edit]
- Non-abelian class field theory
- Special values of L-functions
- Birch-Swinnerton-Dyer
- Bloch-Kato
- Iwasawa "main conjectures"
Relation to other fields[edit]
Notes[edit]
References[edit]
Graduate level accounts[edit]
- Cassels, J. W. S.; Frölich, Albrecht, eds. (1967), Algebraic number theory, London: Academic Press, MR 0215665
- Fröhlich, Albrecht; Taylor, Martin J. (1993), Algebraic number theory, Cambridge Studies in Advanced Mathematics, vol. 27, Cambridge University Press, ISBN 0-521-43834-9, MR 1215934
- Lang, Serge (1994), Algebraic number theory, Graduate Texts in Mathematics, vol. 110 (2 ed.), New York: Springer-Verlag, ISBN 0-387-94225-4, MR 1282723
- Neukirch, Jürgen (1999). Algebraische Zahlentheorie. Grundlehren der mathematischen Wissenschaften. Vol. 322. Berlin: Springer-Verlag. ISBN 978-3-540-65399-8. MR 1697859. Zbl 0956.11021.