Operations in Milnor K-theory

Details Operations in Milnor K-theory Operations in Milnor K-theory

2008-12-02

arxiv.org/abs/0812.0481v1

Mathematics

K-Theory and Homology

to appear in the Journal of Pure and Applied Algebra

Scientific paper

We show that operations in Milnor K-theory mod $p$ of a field are spanned by divided power operations. After giving an explicit formula for divided power operations and extending them to some new cases, we determine for all fields $k$ and all prime numbers $p$, all the operations $K^M_i/p \to K^M_j/p$ commuting with field extensions over the base field $k$. Moreover, the integral case is discussed and we determine the operations $K^M_i/p \to K^M_j/p$ for smooth schemes over a field.

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