Algebraic dependence and Milnor K-theory

2022/11/26 by Adam Topaz, Topaz, Adam
Mathematics · #12G99 #12J10 #19D45 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.2211.14665

openalex publication_date 2022/11/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper shows that algebraic (in)dependence is encoded in Milnor K-theory of fields. As an application, we show that the isomorphism type of a field is determined by its Milnor K-theory, up to purely inseparable extensions, in most situations.

Related

• Reconstructing function fields from Milnor K-theory
• Milnor K₂ and field homomorphisms
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• Varieties and pure symbols
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