Introduction to staggered sheaves
Pramod Achar (Louisiana State/Newton Institute)
Wednesday 11th March, 2009 16:00-17:00 Mathematics Building, room 214
Perverse sheaves, introduced around 1980, have many remarkable properties, involving such notions as Poincare-Verdier duality, weight filtrations and "purity," and the celebrated Decomposition Theorem. These properties have made perverse sheaves into an incredibly powerful tool, especially for applications in representation theory. "Staggered sheaves" are a new attempt to duplicate some of these properties in the setting of vector bundles and coherent sheaves. I will discuss the ingredients that go into defining staggered sheaves, state the main results that are known so far, and perhaps speculate on potential applications. This will be an introductory talk: I will not assume any familiarity with perverse or staggered sheaves, and I will try to focus on examples on A^1 or P^1. Some of the results on staggered sheaves are joint work with D. Sage and D. Treumann.