Eric Ahlqvist, Magnus Carlson
Published 2022-07-13Version 1
We give formulas for 3-fold Massey products in the \'etale cohomology of the ring of integers of a number field and use these to find the first known examples of imaginary quadratic fields with class group of $p$-rank two possessing an infinite $p$-class field tower, where $p$ is an odd prime. We also disprove McLeman's $(3,3)$-conjecture.
$3$-class field towers of exact length $3$
On the equivariant and the non-equivariant main conjecture for imaginary quadratic fields
On Manin's conjecture for a certain singular cubic surface over imaginary quadratic fields
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