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arxiv tag for k-theory

edited Mar 5 2010 at 16:09

Steve Huntsman
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edited Nov 6 2009 at 1:30

Denis-Charles Cisinski
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k-theory algebraic-k-theory motivic-cohomology

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asked Nov 5 2009 at 11:31

S1
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Why is Milnor K-theory not ad hoc?

When Milnor introduced in "Algebraic K-Theory and Quadratic Forms" the Milnor K-groups he said that his definition is motivated by Matsumoto's presentation of algebraic $K_2(k)$ for a field $k$ but is in the end purely ad hoc for $n \geq 3$ . My questions are:

What exactly could Milnor prove with these $K$ -groups? What was his motivation except for Matsumoto's theorem?
Why did this ad hoc definition become so important? Why is it so natural?

k-theory algebraic-k-theory