This article deals with the coherence of the model given by the Cohen-Lenstra heuristic philosophy for class groups and also for their generalizations to Tate-Shafarevich groups. More precisely, our first goal is to extend a previous result due to É. Fouvry and J. Klüners which proves that a conjecture provided by the Cohen-Lenstra philosophy implies another such conjecture. As a consequence of our work, we can deduce, for example, a conjecture for the probability laws of -ranks of Selmer groups of elliptic curves. This is compatible with some theoretical works and other classical conjectures.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-3-3,
author = {Christophe Delaunay and Fr\'ed\'eric Jouhet},
title = {The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups},
journal = {Acta Arithmetica},
volume = {166},
year = {2014},
pages = {245-263},
zbl = {1306.11088},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-3-3}
}
Christophe Delaunay; Frédéric Jouhet. The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups. Acta Arithmetica, Tome 166 (2014) pp. 245-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa164-3-3/