English

On constructing weight structures and extending them to idempotent extensions

K-Theory and Homology 2017-01-24 v4

Abstract

We describe a new method for constructing a weight structure ww on a triangulated category CC. For a given CC and ww it allow us to give a fairly comprehensive (and new) description of those triangulated categories consisting of retracts of objects of CC (i.e., of subcategories of the Karoubi envelope of CC that contain CC; we call them idempotent extensions of CC) such that ww extends to them. In particular, any bounded above or below ww extends to any idempotent extension of CC. We also discuss the applications of our results to certain triangulated categories of ("relative") motives.

Keywords

Cite

@article{arxiv.1605.08372,
  title  = {On constructing weight structures and extending them to idempotent extensions},
  author = {Mikhail V. Bondarko and Vladimir A. Sosnilo},
  journal= {arXiv preprint arXiv:1605.08372},
  year   = {2017}
}

Comments

The (erroneous) example in section 3.2 was replaced by a correct one. Section 4 was rewritten

R2 v1 2026-06-22T14:10:30.341Z