Comparing orders of Selmer groups
Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 2, pp. 467-473.

En utilisant la théorie du corps de classes et la théorie de Kummer, nous calculons l’ordre de deux groupes de Selmer, et nous les comparons : le quotient des deux ordres ne dépend que de conditions locales.

Using both class field and Kummer theories, we propose calculations of orders of two Selmer groups, and compare them: the quotient of the orders only depends on local criteria.

@article{JTNB_2005__17_2_467_0,
     author = {Bosca, S\'ebastien},
     title = {Comparing orders of {Selmer} groups},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {467--473},
     publisher = {Universit\'e Bordeaux 1},
     volume = {17},
     number = {2},
     year = {2005},
     doi = {10.5802/jtnb.502},
     mrnumber = {2211302},
     zbl = {1098.11056},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/jtnb.502/}
}
TY  - JOUR
AU  - Bosca, Sébastien
TI  - Comparing orders of Selmer groups
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2005
DA  - 2005///
SP  - 467
EP  - 473
VL  - 17
IS  - 2
PB  - Université Bordeaux 1
UR  - http://www.numdam.org/articles/10.5802/jtnb.502/
UR  - https://www.ams.org/mathscinet-getitem?mr=2211302
UR  - https://zbmath.org/?q=an%3A1098.11056
UR  - https://doi.org/10.5802/jtnb.502
DO  - 10.5802/jtnb.502
LA  - en
ID  - JTNB_2005__17_2_467_0
ER  - 
Bosca, Sébastien. Comparing orders of Selmer groups. Journal de Théorie des Nombres de Bordeaux, Tome 17 (2005) no. 2, pp. 467-473. doi : 10.5802/jtnb.502. http://www.numdam.org/articles/10.5802/jtnb.502/

[1] Henri Cohen, Francisco Diaz y Diaz, Michel Olivier, Counting Cyclic Quartic Extensions of a Number Field. Journal de Théorie des Nombres de Bordeaux 17 (2005), 475–510. | Numdam | MR 2211303 | Zbl 05016570

[2] Georges Gras, Class Field Theory, from theory to practice. Springer Monographs in Mathematics, second edition 2005. | MR 1941965 | Zbl 1019.11032

Cité par Sources :