Geodesic
Degeneracy of some derived categories
Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 23, Tome 400 (2012), pp. 193-207 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice du chapitre de livre

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. 
@article{ZNSL_2012_400_a9,
     author = {A. L. Smirnov},
     title = {Degeneracy of some derived categories},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {193--207},
     year = {2012},
     volume = {400},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a9/}
}
TY  - JOUR
AU  - A. L. Smirnov
TI  - Degeneracy of some derived categories
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 2012
SP  - 193
EP  - 207
VL  - 400
UR  - http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a9/
LA  - en
ID  - ZNSL_2012_400_a9
ER  - 
%0 Journal Article
%A A. L. Smirnov
%T Degeneracy of some derived categories
%J Zapiski Nauchnykh Seminarov POMI
%D 2012
%P 193-207
%V 400
%U http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a9/
%G en
%F ZNSL_2012_400_a9
A. L. Smirnov. Degeneracy of some derived categories. Zapiski Nauchnykh Seminarov POMI, Problems in the theory of representations of algebras and groups. Part 23, Tome 400 (2012), pp. 193-207. http://geodesic.mathdoc.fr/item/ZNSL_2012_400_a9/

[1] M. J. Shai Haran, “Non-additive geometry”, Compos. Math., 143:3 (2007), 618–688 | MR | Zbl

[2] N. Durov, New approach to Arakelov geometry, 16 Apr., 2007, arXiv: 0704.2030v1[math AG] | Zbl

[3] Sv. Pimenov, Computations in generalized rings, Diploma Thesis, 2008

[4] D. Quillen, Homotopical algebra, Lecture Notes Math., 43, 1967 | DOI | MR | Zbl

[5] V. Voevodsky, “$\mathbf A^1$-Homotopy Theory”, Doc. Math. J., 1998, Extra Vol. I, 579–604 | MR | Zbl

[6] A. Smirnov, “Generalized subrings of arithmetic rings”, Zap. Nauchn. Semin. POMI, 349, 2007, 211–241 | MR

[7] M. Hovey, Model categories, Mathematical Surveys and Monographs, 63, AMS, 1999 | MR | Zbl