Abstract
We consider the Grothendieck topologies on low semi-lattices, defined by one family, and the corresponding sheaf cohomology. This is a basis to define and study the left and right cohomologies and the left and right dimensions of the Chu spaces. The construction of Chu spaces allows to characterize a large class of quantities, for example, the dimension of a Noether space or the Krull dimension of a ring, the Lebesgue-type dimensions, as well as to compare them with the cohomology dimensions of the corresponding Chu spaces. We prove existence of spectral sequences of the morphisms of the Chu spaces.
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Original Russian Text © E. E. Skurikhin and A. G. Sukhonos, 2008, published in Matematicheskie Trudy, 2008, Vol. 11, No. 2, pp. 159–186.
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Skurikhin, E.E., Sukhonos, A.G. Grothendieck topologies on Chu spaces. Sib. Adv. Math. 19, 192–210 (2009). https://doi.org/10.3103/S1055134409030055
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DOI: https://doi.org/10.3103/S1055134409030055