We introduce the notion of a baric structure on a triangulated category, as an abstraction of S. Morel's weight truncation formalism for mixed ℓ-adic sheaves. We study these structures on the derived category of G-equivariant coherent sheaves on a G-scheme X. Our main result shows how to endow this derived category with a family of nontrivial baric structures when G acts on X with finitely many orbits.We also describe a general construction for producing a new t-structure on a triangulated category equipped with given t- and baric structures, and we prove that the staggered t-structures on introduced by Achar arise in this way. © The Author(s) 2010. Published by Oxford University Press. All rights reserved. For permissions.
Publication Source (Journal or Book title)
International Mathematics Research Notices
Achar, P., & Treumann, D. (2011). Baric structures on triangulated categories and coherent sheaves. International Mathematics Research Notices, 2011 (16), 3688-3743. https://doi.org/10.1093/imrn/rnq226