Cohen-Lenstra heuristics and the Spiegelungssatz: function fields (Q1434318)

The author gives support to Cohen-Lenstra heuristics for cyclic function fields by showing its consistency with Leopoldt's Spiegelungssatz in this setting. The paper proceeds by reviewing basic function field theory so as to state a version of the Spiegelungssatz, then proves a group-theoretic version for cyclic function fields. Thereafter, the Friedman-Washington formulation of Cohen-Lenstra heuristics for certain function fields is generalized to the cyclic case. Checking compatibility, under an appropriate assumption, then gives the conclusion.