The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups
The Cohen-Lenstra heuristics, moments and $p^j$-ranks of some groups
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某些群体的 Cohen-Lenstra 启发式、矩和 $p^j$ 等级
DOI：
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发表时间：
2013
期刊：
影响因子：
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通讯作者：
F. Jouhet
中科院分区：
文献类型：
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作者：
C. Delaunay;F. Jouhet
本文讨论了Cohen-Lenstra启发式哲学对类群及其对Tate-Shafarevich群的推广所给出的模型的一致性。更确切地说，我们的第一个目标是推广E. Fouvry和J. Kluners证明了由Cohen-Lenstra哲学提供的一个猜想蕴含着另一个这样的猜想。由于我们的工作，我们可以推导出，例如，一个猜想的概率律$p^j$-秩的塞尔默群的椭圆曲线。这与一些理论著作和其他经典著作是一致的。
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. Kluners 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.