Random matrices, the Cohen-Lenstra heuristics, and roots of unity

Abstract

The Cohen-Lenstra-Martinet heuristics predict the frequency with which a fixed finite abelian group appears as an ideal class group of an extension of number fields, for certain sets of extensions of a base field. Recently, Malle found numerical evidence suggesting that their proposed frequency is incorrect when there are unexpected roots of unity in the base field of these extensions. Moreover, Malle proposed a new frequency, which is a much better match for his data. We present a random matrix heuristic (coming from function fields) that leads to a function field version of Malle's conjecture (as well as generalizations of it).

14 pages

References in corpus (2)

• The distribution of sandpile groups of random graphs
• A weighted Möbius function

Cited by in corpus (11)

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• Nonabelian Cohen-Lenstra Heuristics over Function Fields
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• Statistics for Anticyclotomic Iwasawa Invariants of Elliptic Curves
• Some finite abelian group theory and some q-series identities
• On Iwasawa $\lambda$-invariants for abelian number fields and random matrix heuristics
• A weighted Möbius function
• Cohen Lenstra Heuristics for Étale Group Schemes and Symplectic Pairings
• Cohen-Lenstra heuristics and bilinear pairings in the presence of roots of unity
• Presentations of Galois groups of maximal extensions with restricted ramification