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Zap. Nauchn. Sem. 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

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.

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English version:
Journal of Mathematical Sciences (New York), 2013, 192:2, 234–242

Bibliographic databases:

UDC: 512.66
Received: 03.11.2011
Language:

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://www.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{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84884988174}


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