The power operation in the Galois cohomology of a reductive group over a number field

Mikhail Borovoi, Zinovy Reichstein, Philippe Gille

For a connected reductive group $G$ over a local or global field $K$, we define a *diamond* (or *power*) operation $$(ξ,n)\mapsto ξ^{\Diamond n}\,\colon\, H^1(K,G)\times {\mathbb…