 
Summary: STAGGERED tSTRUCTURES ON DERIVED CATEGORIES OF
EQUIVARIANT COHERENT SHEAVES
PRAMOD N. ACHAR
Abstract. Let X be a scheme, and let G be an affine group scheme acting
on X. Under reasonable hypotheses on X and G, we construct a tstructure
on the derived category of Gequivariant coherent sheaves that in many ways
resembles the perverse coherent tstructure, but which incorporates additional
information from the Gaction. Under certain circumstances, this tstructure,
called the "staggered tstructure," has an artinian heart, and its simple ob
jects are particularly easy to describe. We also exhibit two small examples in
which the staggered tstructure is betterbehaved than the perverse coherent
tstructure.
1. Introduction
Let X be a scheme (say, over a field), and let G be an affine group scheme
acting on X. Perverse coherent sheaves are the objects in the heart of a certain
nonstandard tstructure on the bounded derived category of equivariant coherent
sheaves on X, first introduced by Deligne, but now more widely known from an
exposition by Bezrukavnikov [B1]. One key feature of this category, which we
denote P(X), is that it interacts well with GrothendieckSerre duality, just as the
much betterknown category of perverse (constructible) sheaves interacts well with
