# Magnus Carlson: Class groups and Massey products

**Time: **
Wed 2023-05-03 13.15 - 14.15

**Location: **
KTH, 3418

**Participating: **
Magnus Carlson, SU

**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.