Eric Ahlqvist: Massey products and class field towers

Abstract:

In this talk, I will describe how one can compute and leverage the multiplicative structure of the étale cohomology of the ring of integers of a number field to study embedding problems and class field towers. In particular, I will explain how this approach led us to discover the first examples of imaginary quadratic fields with an infinite class field tower in the last remaining case where the unramified Fontaine-Mazur conjecture is not known. Additionally, I will discuss our disproof of McLeman’s \((3,3)\)-conjecture. The talk will include explicit computations using the C library PARI/GP. This is based on joint work with Magnus Carlson.