Geodesic
On constructing weight structures and extending them to idempotent completions
Homology, homotopy, and applications, Tome 20 (2018) no. 1, pp. 37-57.

Voir la notice de l'article provenant de la source International Press of Boston

In this paper we describe a new method for constructing a weight structure $w$ on a triangulated category $\underline{C}$. For a given $\underline{C}$ and $w$ it allows us to give a fairly comprehensive (and new) description of triangulated categories containing $\underline{C}$ as a dense subcategory (i.e., of subcategories of the idempotent completion of $\underline{C}$ that contain $\underline{C}$; we call them idempotent extensions of $\underline{C}$) to which $w$ extends. In particular, any bounded above or below $w$ extends to any idempotent extension of $\underline{C}$; however, we illustrate by an example that $w$ does not extend to the idempotent completion of $\underline{C}$ in general. We also describe an application of our results to certain triangulated categories of (relative) motives.
DOI : 10.4310/HHA.2018.v20.n1.a3
Classification : 14C15, 18B15, 18E30, 18E40
Keywords: weight structure, triangulated category, idempotent completion, Voevodsky motive, Chow motive, Beilinson motive 
@article{HHA_2018_20_1_a2,
     author = {Mikhail V. Bondarko and Vladimir A. Sosnilo},
     title = {On constructing weight structures and extending them to idempotent completions},
     journal = {Homology, homotopy, and applications},
     pages = {37--57},
     publisher = {mathdoc},
     volume = {20},
     number = {1},
     year = {2018},
     doi = {10.4310/HHA.2018.v20.n1.a3},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n1.a3/}
}
TY  - JOUR
AU  - Mikhail V. Bondarko
AU  - Vladimir A. Sosnilo
TI  - On constructing weight structures and extending them to idempotent completions
JO  - Homology, homotopy, and applications
PY  - 2018
SP  - 37
EP  - 57
VL  - 20
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n1.a3/
DO  - 10.4310/HHA.2018.v20.n1.a3
LA  - en
ID  - HHA_2018_20_1_a2
ER  - 
%0 Journal Article
%A Mikhail V. Bondarko
%A Vladimir A. Sosnilo
%T On constructing weight structures and extending them to idempotent completions
%J Homology, homotopy, and applications
%D 2018
%P 37-57
%V 20
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n1.a3/
%R 10.4310/HHA.2018.v20.n1.a3
%G en
%F HHA_2018_20_1_a2
Mikhail V. Bondarko; Vladimir A. Sosnilo. On constructing weight structures and extending them to idempotent completions. Homology, homotopy, and applications, Tome 20 (2018) no. 1, pp. 37-57. doi : 10.4310/HHA.2018.v20.n1.a3. http://geodesic.mathdoc.fr/articles/10.4310/HHA.2018.v20.n1.a3/

Cité par Sources :