Baric structures on triangulated categories and coherent sheaves

Details Baric structures on triangulated categories and coherent sheaves Baric structures on triangulated categories and coherent sheaves

2008-08-23

arxiv.org/abs/0808.3209v1

Mathematics

Algebraic Geometry

37 pages

Scientific paper

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 D_G(X) 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 D_G(X) introduced by the first author arise in this way.

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