### Operations in Milnor K-theory, by Charles Vial

[The Jan 25, 2008, version has been updated, March 31]

We show that operations in Milnor K-theory mod p of a field are spanned by
divided power operations. We determine for all fields k and all prime
numbers p, all the operations K^M_i/p -> K^M_j/p commuting with field
extensions over the base field k. The integral case is discussed. Finally,
we determine all the operations K^M_i/p -> K^M_j/p for smooth schemes over
a fixed field.

Charles Vial <C.Vial@dpmms.cam.ac.uk>