Let M be a finitely generated faithful module over a noetherian ring R of dimension d < ¥ and let \mathfrak a \subseteqq R be an ideal. We describe the (finite) set SuppR(H\mathfrak ad (M)) = AssR(H\mathfrak ad (M)) of primes associated to the highest local cohomology module H\mathfrak ad (M) in terms of the local formal behaviour of \mathfrak a . If R is integral and of finite type over a field, SuppR(H\mathfrak ad (M)) is the set of those closed points of X = Spec(R) whose fibre under the normalization morphism n: X¢® X contains points which are isolated in n-1(Spec(R/\mathfrak a)).

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Brodmann, M (2002). *A rigidity result for highest order local cohomology modules.* Archiv der Mathematik, 79(2):87-92.

## Abstract

Let M be a finitely generated faithful module over a noetherian ring R of dimension d < ¥ and let \mathfrak a \subseteqq R be an ideal. We describe the (finite) set SuppR(H\mathfrak ad (M)) = AssR(H\mathfrak ad (M)) of primes associated to the highest local cohomology module H\mathfrak ad (M) in terms of the local formal behaviour of \mathfrak a . If R is integral and of finite type over a field, SuppR(H\mathfrak ad (M)) is the set of those closed points of X = Spec(R) whose fibre under the normalization morphism n: X¢® X contains points which are isolated in n-1(Spec(R/\mathfrak a)).

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## Additional indexing

Item Type: | Journal Article, refereed, original work |
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Communities & Collections: | 07 Faculty of Science > Institute of Mathematics |

Dewey Decimal Classification: | 510 Mathematics |

Language: | English |

Date: | 2002 |

Deposited On: | 27 May 2010 13:30 |

Last Modified: | 05 Apr 2016 13:25 |

Publisher: | Springer |

ISSN: | 0003-889X |

Publisher DOI: | 10.1007/s00013-002-8289-y |

Related URLs: | http://www.ams.org/mathscinet-getitem?mr=1925374 http://www.zentralblatt-math.org/zbmath/search/?q=an%3A1090.13011 |

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