"Perverse coherent sheaves and Grothendieck duality"

	Amnon Yekutieli

abstract:

In this talk I will present a new approach to dualizing complexes on 
schemes. Recall that the original treatment in "Residues and Duality" 
used residual complexes in order to glue dualizing complexes on 
schemes. The new idea is based on the observation that dualizing 
complexes are perverse sheaves (for a suitable perversity) within the 
derived category of coherent sheaves. I will explain the main ideas, 
applications and related problems.

Remarkably this new approach was discovered in the context of 
noncommutative geometry, where residual complexes simply do not exist.