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Recently, the norm-residue homomorphism has been the subject of intense discussions in the K-theoretic community following the proof of the Bloch-Kato conjecture by Voevodsky, Suslin and Rost (see Rost’s lecture at this year’s Arbeitstagung.) The goal of this post is to explain the norm-residue homomorphism in a down to earth ring-theoretic language.

Recently I was trying to understand what’s behind the mysterious condition

for elements () to define an element in the Bloch group. It appears that the condition naturally appears if one studies hyperbolic -manifolds.

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