Comparison of Dualizing Complexes, by Changlong Zhong

We prove that there is a map from Bloch's cycle complex to Kato's complex of Milnor K-theory, which induces a quasi-isomorphism from ├ętale sheafified cycle complex to the Gersten complex of logarithmic de Rham-Witt sheaves. Next we show that the truncation of Bloch's cycle complex at -3 is quasi-isomorphic to Spiess' dualizing complex.

UPDATE 2011-04-04: a new version was uploaded, replacing the version dated 2010-11-11. In the new version we add a new section (Section 4) comparing Bloch's complex with Sato's complex. Other important changes include adding the Beilinson-Lichtenbaum Conjecture (Theorem 2.3) and Kummer isomorphism (Theorem 2.6), correction of proofs of Theorem 3.8 and Corollary 3.9 and the notation of the Borel-Moore homology defined by cycle complex.

UPDATE 2011-09-23: a new version was uploaded, replacing the version dated 2011-04-04. In the new version, we correct a mistake found by the referee. Theorem 1.3, Theorem 2.5 (the Beilinson-Lichtenbaum Conjecture) and Theorem 2.6 (Kummer isomorphism) are now proved subject to some truncation condition. The structure of proofs in section 3 and section 4 have a slight change.


Changlong Zhong <czhong@usc.edu>