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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.

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International Mathematics Research Notices

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