Arithmetic Study Group: Class groups of "random" number fields
6 February 2018 14:00 in CM219
The Cohen-Lenstra heuristics, postulated in the early 1980s, say that the sequence of ideal class groups of imaginary quadratic number fields can be modelled as a sequence of random finite abelian groups, where a finite abelian group gets a probability weight that is inversely proportional to the size of its automorphism group. They also propose a model for class groups of real quadratic fields. This was extended in the early 1990s by Cohen-Martinet to much more general families of number fields. I will present very recent joint work with Hendrik Lenstra, in which we are trying to understand the Cohen-Lenstra-Martinet heuristics better. Among other things, this entails disproving them and proposing corrected versions.