Comparison of Dualizing Complexes

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 '{e}tale 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.

💡 Research Summary

The paper investigates two central objects in arithmetic geometry – Bloch’s cycle complex and Kato’s Milnor K‑theory complex – and establishes precise links between them that have significant consequences for duality theory. After recalling the role of dualizing complexes in the study of arithmetic schemes, the author constructs a natural morphism
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