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

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 E. 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.
Document type :
Preprints, Working Papers, ...
Domain :

https://hal.archives-ouvertes.fr/hal-00806518
Contributor : Christophe Delaunay <>
Submitted on : Monday, April 1, 2013 - 10:57:14 AM
Last modification on : Wednesday, December 12, 2018 - 3:17:16 PM

### Identifiers

• HAL Id : hal-00806518, version 1
• ARXIV : 1303.7337

### Citation

Christophe Delaunay, Frédéric Jouhet. The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups. 2013. 〈hal-00806518〉

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