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(2009 / vol.11 / no.1)
Transfer maps for motivic cohomology and Nesterenko-Suslin theorem
Sung Myung
Pages. 1-32   



In this expository article, we first introduce the Milnor's $K$-groups and the Goodwillie groups.
Then, transfer maps, sometimes called norm maps, for Milnor's $K$-theory and for the Goodwillie group are introduced.
The natural transfer maps for the Goodwillie groups, which are easily defined, actually agree with
the classical but difficult transfer maps for the Milnor's $K$-theory.
A by-product of this result will be a proof that Milnor's $K$-groups of fields is isomorphic to the Goodwillie groups.
This result is analogous to one of the most important theorem in algebraic $K$-theory that
motivic cohomology groups of fields, when the degree is equal to the weight,
are isomorphic to Milnor's $K$-groups of fields, which was proved by Nesterenko and Suslin (1989).
The present article is expository and reasonably self-contained.



1. Introduction
2. Milnor's $K$-groups and some computations of symbols
3. Transfer maps for Milnor's $K$-groups
4. Introduction to the Goodwillie groups
5. Some fundamental properties of the Goodwillie group
6. The transfer maps for the Goodwillie group and the Nesterenko-Suslin theorem