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arXiv · 1507.03035

Principal ideals in mod-$\ell$ Milnor $K$-theory

Charles Weibel·Inna Zakharevich
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Abstract

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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Charles Weibel, Inna Zakharevich. 2015-07-10. Principal ideals in mod-$\ell$ Milnor $K$-theory. https://arxiv.org/abs/1507.03035

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