We consider a degenerate abelian variety of CM type. Then there exists such that the ring of Hodge cycles on is not generated by the divisor classes. We call the minimum of such the index of degeneracy of .
In this paper, we determine the index of degeneracy for a certain type of CM abelian varieties. This supplements a former result of H. W. Lenstra, Jr.
Nous considérons une variété abélienne dégénérée de type CM. Alors il existe tel que l’anneau des cycles de Hodge sur n’est pas engendré par les classes de diviseurs. Nous appelons le plus petit vérifiant cette propriété l’indice de dégénérescence de .
Dans cet article, nous déterminons l’indice de dégénérescence d’un certain type de variétés abéliennes de type CM. Cela complète un résultat antérieur de H. W. Lenstra, Jr.
Keywords: Abelian variety, CM-type, Hodge cycle.
@article{JTNB_2015__27_3_815_0,
author = {Hiromichi Yanai},
title = {On the index of degeneracy of a {CM} abelian variety},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {815--820},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {27},
number = {3},
year = {2015},
doi = {10.5802/jtnb.925},
language = {en},
url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.925/}
}
TY - JOUR AU - Hiromichi Yanai TI - On the index of degeneracy of a CM abelian variety JO - Journal de théorie des nombres de Bordeaux PY - 2015 SP - 815 EP - 820 VL - 27 IS - 3 PB - Société Arithmétique de Bordeaux UR - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.925/ DO - 10.5802/jtnb.925 LA - en ID - JTNB_2015__27_3_815_0 ER -
%0 Journal Article %A Hiromichi Yanai %T On the index of degeneracy of a CM abelian variety %J Journal de théorie des nombres de Bordeaux %D 2015 %P 815-820 %V 27 %N 3 %I Société Arithmétique de Bordeaux %U https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.925/ %R 10.5802/jtnb.925 %G en %F JTNB_2015__27_3_815_0
Hiromichi Yanai. On the index of degeneracy of a CM abelian variety. Journal de théorie des nombres de Bordeaux, Volume 27 (2015) no. 3, pp. 815-820. doi : 10.5802/jtnb.925. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.925/
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