Reconstructing function fields from Milnor K-theory

2018/08/15 by Cadoret, Anna, Pirutka, Alena · 1 citation
#Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1808.04944

Abstract

Let F be a finitely generated regular field extension of transcendence degree ≥ 2 over a perfect field k. We show that the multiplicative group F^×/k^× 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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