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.
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.
@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},
zbl = {1098.11056},
mrnumber = {2211302},
language = {en},
url = {http://archive.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 SP - 467 EP - 473 VL - 17 IS - 2 PB - Université Bordeaux 1 UR - http://archive.numdam.org/articles/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, Volume 17 (2005) no. 2, pp. 467-473. doi : 10.5802/jtnb.502. http://archive.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 | Zbl
[2] Georges Gras, Class Field Theory, from theory to practice. Springer Monographs in Mathematics, second edition 2005. | MR | Zbl
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