Conductor (class field theory) (English Wikipedia)

Analysis of information sources in references of the Wikipedia article "Conductor (class field theory)" in English language version.

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11ams.org

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ams.org

mathscinet.ams.org

Serre 1967, §4.2 Serre, Jean-Pierre (1967), "Local class field theory", in Cassels, J. W. S.; Fröhlich, Albrecht (eds.), Algebraic Number Theory, Proceedings of an instructional conference at the University of Sussex, Brighton, 1965, London: Academic Press, ISBN 0-12-163251-2, MR 0220701
As in Neukirch 1999, definition V.1.6 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.
Neukirch 1999, proposition V.1.7 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.
Serre 1967, §4.2, proposition 1 Serre, Jean-Pierre (1967), "Local class field theory", in Cassels, J. W. S.; Fröhlich, Albrecht (eds.), Algebraic Number Theory, Proceedings of an instructional conference at the University of Sussex, Brighton, 1965, London: Academic Press, ISBN 0-12-163251-2, MR 0220701
Artin & Tate 2009, corollary to theorem XI.14, p. 100 Artin, Emil; Tate, John (2009) [1967], Class field theory, American Mathematical Society, ISBN 978-0-8218-4426-7, MR 2467155
As in Serre 1967, §4.2 Serre, Jean-Pierre (1967), "Local class field theory", in Cassels, J. W. S.; Fröhlich, Albrecht (eds.), Algebraic Number Theory, Proceedings of an instructional conference at the University of Sussex, Brighton, 1965, London: Academic Press, ISBN 0-12-163251-2, MR 0220701
Serre 1967, §2.5, proposition 4 Serre, Jean-Pierre (1967), "Local class field theory", in Cassels, J. W. S.; Fröhlich, Albrecht (eds.), Algebraic Number Theory, Proceedings of an instructional conference at the University of Sussex, Brighton, 1965, London: Academic Press, ISBN 0-12-163251-2, MR 0220701
As in Artin & Tate 2009, §XI.4. This is the situation in which the formalism of local class field theory works. Artin, Emil; Tate, John (2009) [1967], Class field theory, American Mathematical Society, ISBN 978-0-8218-4426-7, MR 2467155
Some authors omit infinite places from the conductor, e.g. Neukirch 1999, §VI.6 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.
For the finite part Neukirch 1999, proposition VI.6.5, and for the infinite part Cohen 2000, definition 3.4.1 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. Cohen, Henri (2000), Advanced topics in computational number theory, Graduate Texts in Mathematics, vol. 193, Springer-Verlag, ISBN 978-0-387-98727-9
Neukirch 1999, corollary VI.6.6 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.

jmilne.org

Milne 2008, I.1.9 Milne, James (2008), Class field theory (v4.0 ed.), retrieved 2010-02-22
Milne 2008, theorem III.3.5 Milne, James (2008), Class field theory (v4.0 ed.), retrieved 2010-02-22
Milne 2008, remark V.3.8 Milne, James (2008), Class field theory (v4.0 ed.), retrieved 2010-02-22
Milne 2008, example V.3.11 Milne, James (2008), Class field theory (v4.0 ed.), retrieved 2010-02-22

worldcat.org

Manin, Yu. I.; Panchishkin, A. A. (2007). Introduction to Modern Number Theory. Encyclopaedia of Mathematical Sciences. Vol. 49 (Second ed.). pp. 155, 168. ISBN 978-3-540-20364-3. ISSN 0938-0396. Zbl 1079.11002.

zbmath.org

As in Neukirch 1999, definition V.1.6 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.
Neukirch 1999, proposition V.1.7 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.
Janusz 1973, pp. 158, 168–169 Janusz, Gerald (1973), Algebraic Number Fields, Pure and Applied Mathematics, vol. 55, Academic Press, ISBN 0-12-380250-4, Zbl 0307.12001
Some authors omit infinite places from the conductor, e.g. Neukirch 1999, §VI.6 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.
Manin, Yu. I.; Panchishkin, A. A. (2007). Introduction to Modern Number Theory. Encyclopaedia of Mathematical Sciences. Vol. 49 (Second ed.). pp. 155, 168. ISBN 978-3-540-20364-3. ISSN 0938-0396. Zbl 1079.11002.
For the finite part Neukirch 1999, proposition VI.6.5, and for the infinite part Cohen 2000, definition 3.4.1 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. Cohen, Henri (2000), Advanced topics in computational number theory, Graduate Texts in Mathematics, vol. 193, Springer-Verlag, ISBN 978-0-387-98727-9
Neukirch 1999, corollary VI.6.6 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.