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We propose a modification to the Cohen--Lenstra prediction for thedistribution of class groups of number fields, which should also apply when thebase field contains non-trivial roots of unity. The underlying heuristicderives from the distribution of 1-eigenspaces in certain generalizedsymplectic groups over finite rings. The motivation for that heuristic comesfrom the function field case. We also give explicit formulas for the newpredictions in several important cases. These are in close accordance withknown data.

A class group heuristic based on the distribution of 1-eigenspaces in matrix groups