Cohomology of partially ordered sets and local cohomology of section rings |
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Authors: | Morten Brun |
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Affiliation: | a Department of Mathematics, University of Bergen, 5008 Bergen, Norway b FB Mathematik/Informatik, Universität Osnabrück, 49069 Osnabrück, Germany |
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Abstract: | 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. |
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Keywords: | Local cohomology Partially ordered set Face rings Sections rings |
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