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INTRODUCTION TO STAGGERED SHEAVES PRAMOD N. ACHAR
 

Summary: INTRODUCTION TO STAGGERED SHEAVES
PRAMOD N. ACHAR
Abstract. This note is an expository account of the theory of staggered
sheaves, based on a series of lectures given by the author at RIMS (Kyoto) in
October 2008.
Perverse sheaves have become a tool of great importance in representation the-
ory, largely because of the remarkable way in which they provide a link between
geometry and algebra. A single perverse sheaf contains information reminiscent of
classical algebraic topology; indeed, the prototypical example of a perverse sheaf
comes from the Goresky­MacPherson theory of "intersection homology." But the
category of perverse sheaves behaves like the module categories typically seen in
representation theory, and some of the most important theorems here are Ext-
vanishing and complete reducibility criteria.
Staggered sheaves, the subject of the present note, were introduced by the author
in [A1] and subsequently studied in a series of papers [AT1, AT2, A2] by the author
and D. Treumann. The category of staggered sheaves also enjoys a long list of re-
markable algebraic properties, resembling the most important properties of perverse
sheaves. Most notably, the category of staggered sheaves is quasi-hereditary and
exhibits "purity" and "decomposition" phenomena. But whereas perverse sheaves
are built out of local systems, staggered sheaves are built out of vector bundles,

  

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

 

Collections: Mathematics