Perverse coherent sheaves and rigid dualizing complexes on schemes

Amnon Yekutieli (Ben Gurion University)

Abstract:
Suppose K is a regular noetherian commutative ring, and A is a finite type commutative K-algebra. Then A has a rigid dualizing complex, which is unique up to a unique rigid isomorphism. Such complexes are known to have good functorial properties.

Now consider a finite type separated scheme over K. We define what is a rigid dualizing complex over X (relative to K). In order to prove existence and uniqueness of such a complex, we introduce the rigid perverse t-structure on the derived category of coherent sheaves on X. Since affine rigid dualizing complexes are pervere sheaves for this t-structure, they can be studied locally.

This is joint work with James Zhang.