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

• Autorzy: Christophe Delaunay , Frédéric Jouhet
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11G05: Elliptic curves over global fields
• 11R29: Class numbers, class groups, discriminants

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2014
• Tom: 164
• Numer: 3
• Strony: 245-263

Daty

wydano

2014

Twórcy

autor

Christophe Delaunay

• Université de Franche-Comté, Laboratoire de Mathématiques de Besançon, CNRS UMR 6623, Facultés des Sciences et Techniques, 16 route de Gray, 25030 Besançon, France

autor

Frédéric Jouhet

• Université de Lyon, CNRS, Université Lyon 1, Institut Camille Jordan, 43, boulevard du 11 novembre 1918, F-69622 Villeurbanne Cedex, France

Identyfikatory

DOI

10.4064/aa164-3-3