2015/10/12 by Mikhail V. Bondarko, Bondarko, Mikhail, Vladimir Sosnilo +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Category Theory (math.CT) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)
paper · pdf · doi:10.48550/arxiv.1510.03403
openalex publication_date 2015/10/12 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28
As we proved earlier, for a triangulated category underlineC endowed\nwith a weight structure w and a triangulated subcategory underlineD of\n underlineC (strongly) generated by cones of a set of morphisms S in the\nheart underlineHw of w there exists a weight structure w' on the\nVerdier quotient underlineC'= underlineC/ underlineD such that the\nlocalization functor underlineC \→ underlineC' is weight-exact (i.e.,\n"respects weights"). The goal of this paper is to find conditions ensuring that\nfor any object of underlineC' of non-negative (resp. non-positive) weights\nthere exists its preimage in underlineC satisfying the same condition; we\ncall a certain stronger version of the latter assumption the left (resp.,\nright) weight lifting property. We prove that these weight lifting properties\nare fulfilled whenever the set S satisfies the corresponding (left or right)\nOre conditions. Moreover, if underlineD is generated by objects of\n underlineHw then any object of underlineHw' lifts to\n underlineHw. We apply these results to obtain some new results on Tate\nmotives and finite spectra (in the stable homotopy category). Our results are\nalso applied to the study of the so-called Chow-weight homology in another\npaper.\n