Erik Ahlqvist: Massey products and class field towers

Abstract: I will present recent joint work with Magnus Carlson, where we provide formulas for 3-fold Massey products in the étale cohomology of the ring of integers of a number field. Using these formulas, we identify the first known examples of imaginary quadratic fields with a class group of p-rank two possessing an infinite p-class field tower, where p is an odd prime. Furthermore, we establish a necessary and sufficient condition, in terms of class groups of p-extensions, for the vanishing of 3-fold Massey products. As a consequence, we offer an elementary and sufficient condition for the infinitude of class field towers of imaginary quadratic fields. Additionally, we disprove McLeman’s (3,3)-conjecture.