A geometric approach to the Cohen-Lenstra heuristics by Aaron Landesman

It is well known to experts that moduli spaces exist whose integer points parameterize n-torsion elements in class groups of quadratic number fields. In particular, counting points of bounded height on these spaces is tantamount to solving cases of the Cohen-Lenstra heuristics. We explain why many of these moduli spaces have the following relatively simple form: They are the quotient of the complement of a hypersurface in affine space by the action of an algebraic group.

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