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.