Abstract
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 cycle complex mod pr to Moser's 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. In the end, we prove that a weak form of the Gersten conjecture implies that Sato's dualizing complex is quasi-isomorphic to Bloch's complex.
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