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Matematicheskie Trudy, 2008, Volume 11, Number 2, Pages 159–186 (Mi mt129)  

This article is cited in 4 scientific papers (total in 4 papers)

Grothendieck topologies on Chu spaces

E. E. Skurikhin, A. G. Sukhonos

Institute of Applied Mathematics, Far-Eastern Branch of the Russian Academy of Sciences
Full-text PDF (287 kB) Citations (4)
References:
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.
Key words: Grothendieck topology, sheaf cohomology, Chu space, cohomological dimension, flabby dimension, Lebesgue-type dimension, spectral sequence.
Received: 06.05.2008
English version:
Siberian Advances in Mathematics, 2009, Volume 19, Issue 3, Pages 192–210
DOI: https://doi.org/10.3103/S1055134409030055
Bibliographic databases:
UDC: 512.667+512.667.5+512.562
Language: Russian
Citation: E. E. Skurikhin, A. G. Sukhonos, “Grothendieck topologies on Chu spaces”, Mat. Tr., 11:2 (2008), 159–186; Siberian Adv. Math., 19:3 (2009), 192–210
Citation in format AMSBIB
\Bibitem{SkuSuk08}
\by E.~E.~Skurikhin, A.~G.~Sukhonos
\paper Grothendieck topologies on Chu spaces
\jour Mat. Tr.
\yr 2008
\vol 11
\issue 2
\pages 159--186
\mathnet{http://mi.mathnet.ru/mt129}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2500129}
\elib{https://elibrary.ru/item.asp?id=11715525}
\transl
\jour Siberian Adv. Math.
\yr 2009
\vol 19
\issue 3
\pages 192--210
\crossref{https://doi.org/10.3103/S1055134409030055}
\elib{https://elibrary.ru/item.asp?id=15295685}
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  • https://www.mathnet.ru/eng/mt129
  • https://www.mathnet.ru/eng/mt/v11/i2/p159
  • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические труды Siberian Advances in Mathematics
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    Abstract page:472
    Full-text PDF :173
    References:61
    First page:9
     
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