Notes on exotic and perverse-coherent sheaves

TL;DR

This paper explores exotic and perverse-coherent sheaves on the cotangent bundle of flag varieties, providing definitions, structural insights, applications, and detailed calculations for SL(2).

Contribution

It offers a comprehensive exposition of exotic and perverse-coherent sheaves, including new structural results and explicit calculations for SL(2).

Findings

Definitions and relationships of exotic and perverse-coherent sheaves clarified.

Structural properties and applications discussed.

Explicit calculations for SL(2) provided.

Abstract

Exotic sheaves are certain complexes of coherent sheaves on the cotangent bundle of the flag variety of a reductive group. They are closely related to perverse-coherent sheaves on the nilpotent cone. This expository article includes the definitions of these two categories, applications, and some structure theory, as well as detailed calculations for SL(2).