Translator Disclaimer
VOL. 86 | 2020 Iwasawa-Cohen-Lenstra heuristics
Cornelius Greither

Editor(s) Masato Kurihara, Kenichi Bannai, Tadashi Ochiai, Takeshi Tsuji

Abstract

In this note we propose an analog of the well-known Cohen-Lenstra heuristics for modules over the Iwasawa algebra $\Lambda$. It turns out that only the analog of the real-quadratic situation leads to a convergent series and hence to potential predictions. We determine the sum of this series, which runs over all isomorphism classes of finite $\Lambda$-modules, and we discuss the partial sum that arises by restricting to cyclic $\Lambda$-modules. We demonstrate that this subsum is almost as large as the total sum. No attempt is made to test the heuristics numerically.

Information

Published: 1 January 2020
First available in Project Euclid: 12 January 2021

zbMATH: 1075.11070

Digital Object Identifier: 10.2969/aspm/08610303

Subjects:
Primary: 11R23 , 13H05

Keywords: $\Lambda$-modules , Cohen Lenstra heuristics , Iwasawa theory

Rights: Copyright © 2020 Mathematical Society of Japan

PROCEEDINGS ARTICLE
13 PAGES

This article is only available to subscribers.
It is not available for individual sale.
+ SAVE TO MY LIBRARY

SHARE
RIGHTS & PERMISSIONS
Get copyright permission
Back to Top