The Massey vanishing conjecture for number fields

Yonatan Harpaz (1, 2) , Olivier Wittenberg (1, 2)

1 CNRS - Centre National de la Recherche Scientifique
2 LAGA - Laboratoire Analyse, Géométrie et Applications

A conjecture of Mináč and Tân predicts that for any n>2, any prime p and any field k, the Massey product of n Galois cohomology classes in H¹(k,Z/pZ) must vanish if it is defined. We establish this conjecture when k is a number field.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Yonatan Harpaz, Olivier Wittenberg. The Massey vanishing conjecture for number fields. Duke Mathematical Journal, 2023, 172 (1), pp.1-41. ⟨10.1215/00127094-2022-0004⟩. ⟨hal-02370010⟩