 
Summary: BARIC STRUCTURES ON TRIANGULATED CATEGORIES AND
COHERENT SHEAVES
PRAMOD N. ACHAR AND DAVID TREUMANN
Abstract. 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 Db
G(X) of
Gequivariant coherent sheaves on a Gscheme 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 tstructure on
a triangulated category equipped with given t and baric structures, and we
prove that the staggered tstructures on Db
G(X) introduced by the first author
arise in this way.
1. Introduction
Let Z be a variety over a finite field. The triangulated category of adic sheaves
on X has a full subcategory Db
m(Z) of "mixed sheaves," defined in terms of eigen
values of the Frobenius morphism. The existence and good formal properties of
