GALOIS MODULE STRUCTURE OF GALOIS COHOMOLOGY

NICOLE LEMIRE JAN MINAC JOHN SWALLOW

Abstract. Let F be a field containing a primitive pth root of unity, and let U be an open normal subgroup of index p of the absolute Galois group G_{F} of F. We determine the structure of the cohomology group H^{n}(U, 𝔽_{p}) as an 𝔽_{p}[G_{F} /U]- module for all n ∈ ℕ. Previously this structure was known only for n = 1, and until recently the structure even of H^{1}(U, 𝔽_{p}) was determined only for F a local field, a case settled by Borevič and Faddeev in the 1960s.