Shank, RJ and Fleischmann, P. and Kemper, G.
(2004)
*On the depth of cohomology modules.*
Quarterly Journal of Mathematics, 55
(2).
pp. 167-184.
ISSN 0033-5606.
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Official URL http://dx.doi.org/10.1093/qmath/hag046 |

## Abstract

We study the cohomology modules H-i(G,R) of a p-group G acting on a ring R of characteristic p, for i>0. In particular, we are interested in the Cohen-Macaulay property and the depth of H-i(G,R) regarded as an R-G-module. We first determine the support of H-i(G,R), which turns out to be independent of i. Then we study the Cohen-Macaulay property for H-1(G,R). Further results are restricted to the special case that G is cyclic and R is the symmetric algebra of a vector space on which G acts. We determine the depth of H-i(G,R) for i odd and obtain results in certain cases for i even. Along the way, we determine the degrees in which the transfer map Tr-G R -->R-G has non-zero image.

Item Type: | Article |
---|---|

Uncontrolled keywords: | INVARIANT RINGS |

Subjects: | Q Science > QA Mathematics (inc Computing science) |

Divisions: | Faculties > Science Technology and Medical Studies > School of Mathematics Statistics and Actuarial Science |

Depositing User: | Judith Broom |

Date Deposited: | 19 Dec 2007 18:17 |

Last Modified: | 14 Jan 2010 13:58 |

Resource URI: | http://kar.kent.ac.uk/id/eprint/497 (The current URI for this page, for reference purposes) |

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