#### DOCUMENTA MATHEMATICA,
Extra Volume: Kazuya Kato's Fiftieth Birthday (2003), 479-538

** Uwe Jannsen and Shuji Saito **
Kato Homology of Arithmetic Schemes
and Higher Class Field Theory
over Local Fields

For arithmetical schemes $X$, K. Kato introduced certain complexes
$C^{r,s}(X)$ of Gersten-Bloch-Ogus type whose components involve
Galois cohomology groups of all the residue fields of $X$. For
specific $(r,s)$, he stated some conjectures on their homology
generalizing the fundamental isomorphisms and exact sequences
for Brauer groups of local and global fields. We prove some of
these conjectures in small degrees and give applications to the
class field theory of smooth projecive varieties over
local fields, and finiteness questions for some motivic cohomology
groups over local and global fields.

2000 Mathematics Subject Classification: 11G25, 11G45, 14F42

Keywords and Phrases: Kato homology, Bloch-Ogus theory, niveau spectral sequence, arithmetic
homology, higher class field theory

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