Duality via cycle complexes


We show that Bloch’s complex of relative zero-cycles can be used as a dualizing complex over perfect fields and number rings. This leads to duality theorems for torsion sheaves on arbitrary separated schemes of finite type over algebraically closed fields, finite fields, local fields of mixed characteristic, and rings of integers in number rings, generalizing results which so far have only been known for smooth schemes or in low dimensions, and unifying the $p$-adic and $l$-adic theory. As an application, we generalize Rojtman’s theorem to normal, projective schemes.


Thomas Geisser

Department of Mathematics
University of Southern California
3620 South Vermont Ave.
KAP 108
Los Angeles, CA 90089-2532
United States