Baric Structures on Triangulated Categories and Coherent Sheaves

We introduce the notion of a baric structure on a triangulated category, as an abstraction of S. Morel's weight truncation formalism for mixed -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 t...

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Bibliographic Details
Published in:International mathematics research notices 2011-01, Vol.2011 (16), p.3688-3743, Article 3688
Main Authors: Achar, Pramod N., Treumann, David
Format: Article
Language:English
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Summary:We introduce the notion of a baric structure on a triangulated category, as an abstraction of S. Morel's weight truncation formalism for mixed -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.
ISSN:1073-7928
1687-0247
DOI:10.1093/imrn/rnq226