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},
zbl = {1098.11056},
mrnumber = {2211302},
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 SP - 467 EP - 473 VL - 17 IS - 2 PB - Université Bordeaux 1 UR - http://www.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, 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 | Zbl
[2] Georges Gras, Class Field Theory, from theory to practice. Springer Monographs in Mathematics, second edition 2005. | MR | Zbl
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