Cohen-Lenstra heuristics and . . .

In 1984 Cohen and Lenstra [5] published a set of conjectures about the distribution of class groups of quadratic number fields. Now dubbed the `Cohen-Lenstra Heuristics', these conjectures state that for a given finite abelian group A, the probability that a random quadratic number eld has class group isomorphic to A is inversely proportional to the size of the automorphism group of A. In a recent paper, Ellenberg, Venkatesh and Westerland [6] used homological stability theorems to prove a similar heuristic over quadratic extensions of function fields. We will introduce the Cohen-Lenstra heuristics and group homology, then attempt to verify homological stabilit