Reconstructing function fields from Milnor K-theory

Anna Cadoret; Alena Pirutka

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arXiv · 1808.04944

Reconstructing function fields from Milnor K-theory

Anna Cadoret·Alena Pirutka

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Abstract

Let $F$ be a finitely generated regular field extension of transcendence degree $\geq 2$ over a perfect field $k$. We show that the multiplicative group $F^\times/k^\times$ endowed with the equivalence relation induced by algebraic dependence on $k$ determines the isomorphism class of $F$ in a functorial way. As a special case of this result, we obtain that the isomorphism class of the graded Milnor $K$-ring $K^M_*(F)$ determines the isomorphism class of $F$, when $k$ is algebraically closed or finite.

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Anna Cadoret, Alena Pirutka. 2018-08-15. Reconstructing function fields from Milnor K-theory. https://arxiv.org/abs/1808.04944

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