Abstract

For a finite group G, a G-module M, and a field F, an element u∈Hd(G,M) is negligible over F if for each field extension L/F and every continuous group homomorphism from Gal(Lsep/L) to G, u belongs to the kernel of the induced homomorphism Hd(G,M)→Hd(L,M). For p a prime and a trivial G-action on the coefficients, the negligible elements in the cohomology ring H⁎(G,Z/pZ) form an ideal. We compute the generators of the negligible ideal in the mod p cohomology of elementary abelian p-groups. We further show that when p is odd or p=2 and either |G| is odd or F is not formally real, the Krull dimension of the quotient of mod p cohomology by the negligible ideal is 0. However, when p=2, |G| is even, and F is formally real, the Krull dimension of the quotient of mod 2 cohomology of a finite 2-group by the negligible ideal is 1.

Full Text
Paper version not known

Talk to us

Join us for a 30 min session where you can share your feedback and ask us any queries you have

Schedule a call

Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.