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arXiv · 1604.03433

Nonabelian Cohen-Lenstra Heuristics over Function Fields

Nigel Boston·Melanie Matchett Wood
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Abstract

Boston, Bush, and Hajir have developed heuristics, extending the Cohen-Lenstra heuristics, that conjecture the distribution of the Galois groups of the maximal unramified pro-p extensions of imaginary quadratic number fields for p an odd prime. In this paper, we find the moments of their proposed distribution, and further prove there is a unique distribution with those moments. Further, we show that in the function field analog, for imaginary quadratic extensions of F_q(t), the Galois groups of the maximal unramified pro-p extensions, as q goes to infinity, have the moments predicted by the Boston, Bush, and Hajir heuristics. In fact, we determine the moments of the Galois groups of the maximal unramified pro-odd extensions of imaginary quadratic function fields, leading to a conjecture on Galois groups of the maximal unramified pro-odd extensions of imaginary quadratic number fields.

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Nigel Boston, Melanie Matchett Wood. 2016-04-12. Nonabelian Cohen-Lenstra Heuristics over Function Fields. https://doi.org/10.1112/s0010437x17007102

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