Geodesic
A Generalization of Global Class Field Theory
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 609-614

Voir la notice de l'article provenant de la source Cambridge University Press

Let R be a field of rational functions of one variable over a field of constants R 0. Dock Sang Rim (6) has proved that the global reciprocity law in exactly the usual sense holds whenever R 0 is an absolutely algebraic quasi-fini te field of characteristic not equal to 0: this was known before only when R 0 was a finite field. We shall give another proof of Rim's result by means of a noteworthy generalization of the usual global reciprocity law. Namely, let R 0 be a finite field and let F be the set of all fields k contained in some fixed R alg.clos. and of finite degree over R. The reciprocity law states that there exists a family {fk }, k ∈ F, of functions fk : Ck → G(k abel.clos./k) (where Ck is the idèle class group of k) enjoying certain properties such as the norm transfer law. 
Seo, Tae Kun; Whaples, G. A Generalization of Global Class Field Theory. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 609-614. doi: 10.4153/CJM-1969-069-8
@article{10_4153_CJM_1969_069_8,
     author = {Seo, Tae Kun and Whaples, G.},
     title = {A {Generalization} of {Global} {Class} {Field} {Theory}},
     journal = {Canadian journal of mathematics},
     pages = {609--614},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-069-8},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-069-8/}
}
TY  - JOUR
AU  - Seo, Tae Kun
AU  - Whaples, G.
TI  - A Generalization of Global Class Field Theory
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 609
EP  - 614
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-069-8/
DO  - 10.4153/CJM-1969-069-8
ID  - 10_4153_CJM_1969_069_8
ER  - 
%0 Journal Article
%A Seo, Tae Kun
%A Whaples, G.
%T A Generalization of Global Class Field Theory
%J Canadian journal of mathematics
%D 1969
%P 609-614
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-069-8/
%R 10.4153/CJM-1969-069-8
%F 10_4153_CJM_1969_069_8

[1] 1. Artin, E., Algebraic numbers and algebraic functions. I, Mimeographed lecture notes, Princeton University, Princeton, N.J. ; New York University, New York, 1951 (printed éd., Gordon and Breach, New York, 1967). Google Scholar

[2] 2. Artin, E. and Tate, J., Class field theory, Lecture notes, Harvard University, Cambridge, Massachusetts, 1961 (W. A. Benjamin, New York, 1968). Google Scholar

[3] 3. Kawada, Y., On the class field theory on algebraic number fields with infinite degree, J. Math. Soc. Japan 8 (1951), 104–115. Google Scholar

[4] 4. Kawada, Y., Class formations. IV (infinite extension of ground field), J. Math. Soc. Japan 9 (1957), 395–405. Google Scholar

[5] 5. Mori, M., Ueber Klas s enkôrper théorie fur unendliche Erweiterungen von einem p-adischen Zahlkôrper, Proc. Japan Acad. 33 (1957), 376–379. Google Scholar

[6] 6. Rim, D. S. and Whaples, G., A remark on quasi-finite field, Nagoya Math. J. 27 (1966), 323–329. Google Scholar

[7] 7. Kun Seo, Tae, A generalization of global class field theory, Ph.D. Thesis, Indiana University, Bloomington, Indiana, 1965. Google Scholar

[8] 8. Whaples, G., Lecture notes on class field theory, Bowdoin College, Summer, 1966. Google Scholar

Cité par Sources :