Staggered t-structures on derived categories of equivariant coherent sheaves

TL;DR

This paper introduces the staggered t-structure on derived categories of G-equivariant coherent sheaves, extending the perverse coherent t-structure by incorporating G-action, with applications to better-behaved structures in specific examples.

Contribution

It constructs a new t-structure called the staggered t-structure that generalizes the perverse coherent t-structure to include G-action, with a focus on its properties and examples.

Findings

The staggered t-structure has an artinian heart.

Simple objects in the heart are explicitly describable.

In certain cases, it outperforms the perverse coherent t-structure.

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 objects 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.