Magnus Carlson: Class groups and Massey products

Abstract

In this talk I will explain how to compute Massey products in the étale cohomology of a number field K in terms of arithmetic data coming from extensions of K. I will then explain how to use Massey products to study the classical number-theoretical problem of class field towers:w I will show how one can use Massey products to find the first known examples of an infinite p-class field tower for an imaginary quadratic number field of p-rank two (p an odd prime). I will also talk about how the vanishing of Massey products control the rank of certain class groups.

This talk is based on joint work with Eric Ahlqvist.