Papers › Massey products in the étale cohomology of number fields
Massey products in the étale cohomology of number fields
Eric Ahlqvist, Magnus Carlson
The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.
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. Furthermore, a necessary and sufficient condition, in terms of class groups of p-extensions, for the vanishing of 3-fold Massey products is given. As a consequence, we give an elementary and sufficient condition for the infinitude of class field towers of imaginary quadratic fields. We also disprove McLeman's (3,3)-conjecture. Lastly, we relate the vanishing of Massey products to the existence of Galois representations of G_(ℚ,S) which realize an unexpectedly large class group for certain extensions of a quadratic imaginary number field.
Code
Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.
Code Syntology ran Syntology
Not run by Syntology. Nothing on this page verifies that the listed code works.
Results from the paper archive 2025-07-28
No leaderboard rows for this paper in the archive.
Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections