Cohomology of partially ordered sets and local cohomology of section rings
arXiv:math/0502517 · doi:10.1016/j.aim.2006.02.005
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.
24 pages; To appear in Adv. Math. Revised version of the paper
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Cited by in corpus (14)
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- (Co)homology theories for structured spaces arising from their corresponding poset
- A (co)homology theory for some preordered topological spaces
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