Cohomology of partially ordered sets and local cohomlogy of section rings
Autor(en): | Brun, Morten Bruns, Winfried Roemer, Tim |
Stichwörter: | face rings; local cohomology; Mathematics; partially ordered set; sections rings | Erscheinungsdatum: | 2007 | Herausgeber: | ACADEMIC PRESS INC ELSEVIER SCIENCE | Journal: | ADVANCES IN MATHEMATICS | Volumen: | 208 | Ausgabe: | 1 | Startseite: | 210 | Seitenende: | 235 | Zusammenfassung: | We study local cohomology of rings of global sections of sheafs on the Alexandrov space of a partially ordered set. We give a criterion for a splitting of the local cohomology groups into summands determined by the cohomology of the poset and the local cohomology of the stalks. The face ring of a rational pointed fan can be considered as the ring of global sections of a flasque sheaf on the face poset of the fan. Thus we obtain a decomposition of the local cohomology of such face rings. Since the Stanley-Reisner ring of a simplicial complex is the face ring of a rational pointed fan, our main result can be interpreted as a generalization of Hochster's decomposition of local cohomology of Stanley-Reisner rings. (c) 2006 Elsevier Inc. All rights reserved. |
ISSN: | 00018708 | DOI: | 10.1016/j.aim.2006.02.005 |
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