Commit 2026-01-05 14:32 f04c5aee

feat(RepresentationTheory/Homological/GroupCohomology/Hilbert90): add Hilbert 90 for cyclic groups (#33124) Let L/K be a finite extension of fields. Noether's generalization of Hilbert's Theorem 90 is that the 1st group cohomology $H^1(Aut_K(L), L^\times)$ is trivial. Hilbert's original statement was that if $L/K$ is Galois, and $Gal(L/K)$ is cyclic, generated by an element σ, then for every x : L such that $N_{L/K}(x) = 1,$ there exists y : L such that $x = y/σ(y)$. We prove that in this PR, using the fact that H¹(G, A) ≅ Ker(N_A)/(ρ(g) - 1)(A) for any finite cyclic group G with generator g, and then applying Noether's generalization.