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

Christophe DelaunayFrédéric Jouhet — 2014

Acta Arithmetica

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...

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