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Summary: STAGGERED SHEAVES ON PARTIAL FLAG VARIETIES
PRAMOD N. ACHAR AND DANIEL S. SAGE
Abstract. Staggered t-structures are a class of t-structures on derived categories of equivariant co-
herent sheaves. In this note, we show that the derived category of coherent sheaves on a partial flag
variety, equivariant for a Borel subgroup, admits an artinian staggered t-structure. As a consequence,
we obtain a basis for its equivariant K-theory consisting of simple staggered sheaves.
Let X be a variety over an algebraically closed field, and let G be an algebraic group acting on X
with finitely many orbits. Let CohG
(X) be the category of G-equivariant coherent sheaves on X, and let
DG
(X) denote its bounded derived category. Staggered sheaves, introduced in [1], are the objects in the
heart of a certain t-structure on DG
(X), generalizing the perverse coherent t-structure [2]. The definition
of this t-structure depends on the following data: (1) an s-structure on X (see below); (2) a choice of a
SerreGrothendieck dualizing complex X DG
(X) [4]; and (3) a perversity, which is an integer-valued
function on the set of G-orbits, subject to certain constraints. When the perversity is "strictly monotone
and comonotone," the category of staggered sheaves is particularly nice: every object has finite length,
and every simple object arises by applying an intermediate-extension ("IC") functor to an irreducible
vector bundle on a G-orbit.
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