Comparison of Dualizing Complexes

Abstract

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 étale 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.

arXiv comment34 pages, 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