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Search: MSC category 19D45 ( Higher symbols, Milnor $K$-theory )

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1. CMB 2005 (vol 48 pp. 221)

Kerr, Matt
An Elementary Proof of Suslin Reciprocity
We state and prove an important special case of Suslin reciprocity that has found significant use in the study of algebraic cycles. An introductory account is provided of the regulator and norm maps on Milnor $K_2$-groups (for function fields) employed in the proof.

Categories:19D45, 19E15

2. CMB 2005 (vol 48 pp. 237)

Kimura, Kenichiro
Indecomposable Higher Chow Cycles
Let $X$ be a projective smooth variety over a field $k$. In the first part we show that an indecomposable element in $CH^2(X,1)$ can be lifted to an indecomposable element in $CH^3(X_K,2)$ where $K$ is the function field of 1 variable over $k$. We also show that if $X$ is the self-product of an elliptic curve over $\Q$ then the $\Q$-vector space of indecomposable cycles $CH^3_{ind}(X_\C,2)_\Q$ is infinite dimensional. In the second part we give a new definition of the group of indecomposable cycles of $CH^3(X,2)$ and give an example of non-torsion cycle in this group.

Categories:14C25, 19D45

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