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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