A geometric approach to the CohenLenstra heuristics
A geometric approach to the CohenLenstra heuristics

Aaron Landesman, Stanford University
The CohenLenstra heuristics in number theory describe the average number of $n$torsion elements in class groups of quadratic fields. We present a geometric approach to these heuristics, which has the following consequence: under the correspondence between quadratic forms and elements of class groups of quadratic fields, a quadratic form $q$ corresponds to an $n$torsion element if and only if there exists a degree $n$ polynomial whose resultant with $q$ is $\pm 1$.This follows from a general structure theorem describing $\mu_n$ torsors over degree $2$ covers, which is based on a classical construction in algebraic geometry.