TY - JOUR

T1 - On constructing weight structures and extending them to idempotent completions

AU - Bondarko, Mikhail V.

AU - Sosnilo, Vladimir A.

PY - 2018/1/1

Y1 - 2018/1/1

N2 - In this paper we describe a new method for constructing a weight structure w on a triangulated category C. For a given C and w it allows us to give a fairly comprehensive (and new) description of triangulated categories containing C as a dense subcategory (i.e., of subcategories of the idempotent completion of C that contain C; we call them idempotent extensions of C) to which w extends. In particular, any bounded above or below w extends to any idempotent extension of C; however, we illustrate by an example that w does not extend to the idempotent completion of C in general. We also describe an application of our results to certain triangulated categories of (relative) motives.

AB - In this paper we describe a new method for constructing a weight structure w on a triangulated category C. For a given C and w it allows us to give a fairly comprehensive (and new) description of triangulated categories containing C as a dense subcategory (i.e., of subcategories of the idempotent completion of C that contain C; we call them idempotent extensions of C) to which w extends. In particular, any bounded above or below w extends to any idempotent extension of C; however, we illustrate by an example that w does not extend to the idempotent completion of C in general. We also describe an application of our results to certain triangulated categories of (relative) motives.

KW - Beilinson motive

KW - Chow motive

KW - Idempotent completion

KW - Triangulated category

KW - Voevodsky motive

KW - Weight structure

UR - http://www.scopus.com/inward/record.url?scp=85042559680&partnerID=8YFLogxK

U2 - 10.4310/HHA.2018.v20.n1.a3

DO - 10.4310/HHA.2018.v20.n1.a3

M3 - Article

AN - SCOPUS:85042559680

VL - 20

SP - 37

EP - 57

JO - Homology, Homotopy and Applications

JF - Homology, Homotopy and Applications

SN - 1532-0073

IS - 1

ER -