[
    {
        "id": "authors:bd6ph-62c84",
        "collection": "authors",
        "collection_id": "bd6ph-62c84",
        "cite_using_url": "https://authors.library.caltech.edu/records/bd6ph-62c84",
        "type": "article",
        "title": "Krull dimension of the negligible quotient in mod p cohomology of a finite group",
        "author": [
            {
                "family_name": "Gherman",
                "given_name": "M.",
                "orcid": "0009-0007-2601-7862",
                "clpid": "Gherman-Matthew-M"
            },
            {
                "family_name": "Merkurjev",
                "given_name": "A.",
                "orcid": "0000-0002-4447-1838"
            }
        ],
        "abstract": "For a finite group G, a G-module M, and a field F, an element u \u2208 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 belongs to the kernel of the induced homomorphism H d ( G , M ) \u2192 H d ( L , M ) . For p a prime and a trivial G-action on the coefficients, the negligible elements in the cohomology ring H \u204e ( G , Z / p Z ) 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.",
        "doi": "10.1016/j.jpaa.2023.107489",
        "issn": "0022-4049",
        "publisher": "Elsevier",
        "publication": "Journal of Pure and Applied Algebra",
        "publication_date": "2024-03",
        "series_number": "3",
        "volume": "228",
        "issue": "3",
        "pages": "107489"
    },
    {
        "id": "authors:h4vaa-m1r93",
        "collection": "authors",
        "collection_id": "h4vaa-m1r93",
        "cite_using_url": "https://authors.library.caltech.edu/records/h4vaa-m1r93",
        "type": "article",
        "title": "Negligible degree two cohomology of finite groups",
        "author": [
            {
                "family_name": "Gherman",
                "given_name": "Matthew",
                "orcid": "0009-0007-2601-7862",
                "clpid": "Gherman-Matthew-M"
            },
            {
                "family_name": "Merkurjev",
                "given_name": "Alexander",
                "orcid": "0000-0002-4447-1838"
            }
        ],
        "abstract": "<p>For a finite group G, a G-module M and a field F, an element u &isin; H d ( G , M ) is negligible over F if for each field extension L / F and every group homomorphism Gal ( L sep / L ) &rarr; G , u belongs to the kernel of the induced homomorphism H d ( G , M ) &rarr; H d ( L , M ) . We determine the group of negligible elements in H 2 ( G , M ) for every abelian group M with trivial G-action.</p>",
        "doi": "10.1016/j.jalgebra.2022.07.039",
        "issn": "0021-8693",
        "publisher": "Elsevier",
        "publication": "Journal of Algebra",
        "publication_date": "2022-12-01",
        "volume": "611",
        "pages": "82-93"
    }
]