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On Carlson's depth conjecture in group cohomology

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Abstract

We establish a weak form of Carlson's conjecture on the depth of the mod-p cohomology ring of a p-group. In particular, Duflot's lower bound for the depth is tight if and only if the cohomology ring is not detected on a certain family of subgroups. The proofs use the structure of the cohomology ring as a comodule over the cohomology of the centre via the multiplication map. We demonstrate the existence of systems of parameters (so-called polarised systems) which are particularly well adapted to this comodule structure.

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  1. Fachbereich 7 Mathematik, Bergische Universität Wuppertal, 42097, Wuppertal, Germany

    David J. Green

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  1. David J. Green
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Correspondence to David J. Green.

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Mathematics Subject Classification (2000): 20J06.

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Green, D. On Carlson's depth conjecture in group cohomology. Math. Z. 244, 711–723 (2003). https://doi.org/10.1007/s00209-003-0517-z

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  • DOI: https://doi.org/10.1007/s00209-003-0517-z

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