Negligible cohomology (Matthew Gherman, Caltech)

For a finite group G, a G-module M, and a field F, an element u in H^d(G,M) is negligible over F if for each field extension L/F and every continuous group homomorphism from Gal(L^{sep}/L) to G, u is in the kernel of the induced homomorphism H^d(G,M) to H^d(L,M). Negligible cohomology was first introduced by Serre and has deep connections with the embedding problem, cohomological invariants, and the profinite inverse Galois problem. Professor Alexander Merkurjev (UCLA) and I were able to compute negligible cohomology in degree 2, compute the mod p negligible cohomology of elementary abelian p-groups, and determine the Krull dimension of the quotient of mod p cohomology by the ideal of negligible elements.