EVENT DETAILS AND ABSTRACT

Title: The category of staggered sheaves
Speaker: Pramod Achar
Speaker Info: LSU
Brief Description:
Special Note:
Abstract:

Let $G$ be an algebraic group, and let $X$ be a variety with a $G$-action. The category of ($G$-equivariant) perverse coherent sheaves on $X$ has shown up in various applications in geometric representation theory. However, this category has good properties only under strong conditions on the $G$-action, conditions that fail on many common spaces, including the flag variety and the Steinberg variety of a reductive group.

I will describe the construction of a $t$-structure on the derived category of equivariant coherent sheaves on $X$ that resembles the perverse coherent $t$-structure, but incorporates additional information from the $G$-action. The resulting abelian category, known as the category of ``staggered sheaves,'' has many desirable properties---e.g., every object has finite length, and simple objects are given by an ``IC'' functor---under weaker conditions than what the perverse coherent category requires. I will also discuss some small examples, and speculate on potential uses of this category in representation theory.