Olivier Wittenberg, Massey products in the Galois cohomology of number fields

(Joint work with Yonatan Harpaz.) Let k be a field and p be a prime. According to a conjecture of Mináč and Tân, Massey products of n (strictly greater than 2) classes in H^1(k,Z/pZ) should vanish whenever they are defined. We establish this conjecture when k is a number field, for any n. This constraint on the absolute Galois group of k was previously known to hold when n=3 and when n=4, p=2.