Geodesic
Duality via cycle complexes
Thomas Geisser1
1Department of Mathematics<br/>University of Southern California<br/>3620 South Vermont Ave.<br/>KAP 108<br/>Los Angeles, CA 90089-2532<br/>United States
Annals of mathematics, Tome 172 (2010) no. 2, pp. 1095-1126
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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.

DOI : 10.4007/annals.2010.172.1095

Thomas Geisser  1

1 Department of Mathematics<br/>University of Southern California<br/>3620 South Vermont Ave.<br/>KAP 108<br/>Los Angeles, CA 90089-2532<br/>United States 
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Thomas Geisser. Duality via cycle complexes. Annals of mathematics, Tome 172 (2010) no. 2, pp. 1095-1126. doi: 10.4007/annals.2010.172.1095

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