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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 400, Pages 193–207 (Mi znsl5618)  
Degeneracy of some derived categories

A. L. Smirnov

St. Petersburg Department of the Steklov Mathematical Institute, Fontanka 27, St. Petersburg 191023, Russia
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Abstract: We study derived categories for the category of the modules over some generalized rings. In particular, the cases of $\mathcal O_\mathbb R$ and of $\mathbb F_{1^n}$ are considered. It is shown that these derived categories are degenerate. The degeneracy means that every isomorphism in such a category can be detected on the $\pi_0$- and $\pi^0$-levels.
Key words and phrases: field with one element, generalized ring, derived category, direct image, simplicial, cosimplicial, Archimedean, Dold–Kan.
Received: 03.11.2011
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 192, Issue 2, Pages 234–242
DOI: https://doi.org/10.1007/s10958-013-1388-4
Bibliographic databases:
Document Type: Article
UDC: 512.66
Language: English
Citation: A. L. Smirnov, “Degeneracy of some derived categories”, Problems in the theory of representations of algebras and groups. Part 23, Zap. Nauchn. Sem. POMI, 400, POMI, St. Petersburg, 2012, 193–207; J. Math. Sci. (N. Y.), 192:2 (2013), 234–242
Citation in format AMSBIB
\Bibitem{Smi12}
\by A.~L.~Smirnov
\paper Degeneracy of some derived categories
\inbook Problems in the theory of representations of algebras and groups. Part~23
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 400
\pages 193--207
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5618}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=3029572}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 192
\issue 2
\pages 234--242
\crossref{https://doi.org/10.1007/s10958-013-1388-4}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884988174}
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