Degenerate fourfold Massey products over arbitrary fields

Online seminar on Quadratic forms, Linear algebraic groups and Beyond, Wednesdays 8:30-9:30am

https://uottawa-ca.zoom.us/j/99397061432?pwd=LzNBS1UrSVNJQ1ZiU28yWHAyNlV...

We prove that, for all fields F of characteristic different from 2 and all a,b,c in F, the mod 2 Massey product <a, b, c, a> vanishes as soon as it is defined. For every field E of characteristic different form 2, we construct a field F containing E and a,b,c,d in F such that and vanish but is not defined. As a consequence, we answer a question of Positselski by constructing the first examples of fields containing all roots of unity and such that the mod 2 cochain DGA of the absolute Galois group is not formal. This is joint work with Alexander Merkurjev.