Notes on exotic and perverse-coherent sheaves

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).

33 pages

References in corpus (4)

• Localization of modules for a semisimple Lie algebra in prime characteristic
• Exotic tilting sheaves, parity sheaves on affine Grassmannians, and the Mirkovic-Vilonen conjecture
• Modular representations of reductive groups and geometry of affine Grassmannians
• Modular perverse sheaves on flag varieties I: tilting and parity sheaves