The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups

Christophe Delaunay, and Frédéric Jouhet. "The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups." Acta Arithmetica 164.3 (2014): 245-263. <http://eudml.org/doc/279077>.

@article{ChristopheDelaunay2014,
abstract = {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 $p^j$-ranks of Selmer groups of elliptic curves. This is compatible with some theoretical works and other classical conjectures.},
author = {Christophe Delaunay, Frédéric Jouhet},
journal = {Acta Arithmetica},
keywords = {Cohen-Lenstra heuristics; class group; Selmer group; Tate-Shafarevich group},
language = {eng},
number = {3},
pages = {245-263},
title = {The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups},
url = {http://eudml.org/doc/279077},
volume = {164},
year = {2014},
}

TY - JOUR
AU - Christophe Delaunay
AU - Frédéric Jouhet
TI - The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups
JO - Acta Arithmetica
PY - 2014
VL - 164
IS - 3
SP - 245
EP - 263
AB - 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 $p^j$-ranks of Selmer groups of elliptic curves. This is compatible with some theoretical works and other classical conjectures.
LA - eng
KW - Cohen-Lenstra heuristics; class group; Selmer group; Tate-Shafarevich group
UR - http://eudml.org/doc/279077
ER -