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ON THE QUASI-HEREDITARY PROPERTY FOR STAGGERED SHEAVES
 

Summary: ON THE QUASI-HEREDITARY PROPERTY FOR
STAGGERED SHEAVES
PRAMOD N. ACHAR
Abstract. Let G be an algebraic group over an algebraically closed field, act-
ing on a variety X with finitely many orbits. Staggered sheaves are certain
complexes of G-equivariant coherent sheaves on X that seem to possess many
remarkable properties. In this paper, we construct "standard" and "costan-
dard" objects in the category of staggered sheaves, and we prove that that
category has enough projectives and injectives.
1. Introduction
Let X be a variety over an algebraically closed field k, and let G be a linear
algebraic group over k acting on X with finitely many orbits. Staggered sheaves [A,
AT1] are the objects in the heart of certain t-structure on the bounded derived
category Db
G(X) of G-equivariant coherent sheaves on X. The category of staggered
sheaves, denoted M(X), enjoys a growing list of remarkable properties, analogous
in many ways to properties of -adic mixed perverse sheaves [AT1, AT2]:
Every object has finite length. Simple objects arise via an "IC" functor
and are parametrized by irreducible vector bundles on G-orbits.
There is a well-behaved notion of "purity" in Db

  

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

 

Collections: Mathematics