Principal ideals in mod- $$\ell $$ Milnor K-theory
Tóm tắt
Fix a symbol
$$\underline{a}$$
in the mod-
$$\ell $$
Milnor K-theory of a field k, and a norm variety X for
$$\underline{a}$$
. We show that the ideal generated by
$$\underline{a}$$
is the kernel of the K-theory map induced by
$$k\subset k(X)$$
and give generators for the annihilator of the ideal. When
$$\ell =2$$
, this was done by Orlov, Vishik and Voevodsky.
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