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STAGGERED t-STRUCTURES ON DERIVED CATEGORIES OF EQUIVARIANT COHERENT SHEAVES
 

Summary: STAGGERED t-STRUCTURES 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 t-structure
on the derived category of G-equivariant coherent sheaves that in many ways
resembles the perverse coherent t-structure, but which incorporates additional
information from the G-action. Under certain circumstances, this t-structure,
called the "staggered t-structure," has an artinian heart, and its simple ob-
jects are particularly easy to describe. We also exhibit two small examples in
which the staggered t-structure is better-behaved than the perverse coherent
t-structure.
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 t-structure 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 better-known category of perverse (constructible) sheaves interacts well with

  

Source: Achar, Pramod - Department of Mathematics, Louisiana State University

 

Collections: Mathematics