Reconstructing function fields from Milnor K-theory

Anna Cadoret, Alena Pirutka

Research output: Contribution to journalArticlepeer-review


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 F over 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.

Original languageEnglish (US)
Pages (from-to)2261-2288
Number of pages28
JournalAlgebra and Number Theory
Issue number9
StatePublished - 2021


  • Function fields
  • Milnor K-theory
  • Reconstruction

ASJC Scopus subject areas

  • Algebra and Number Theory


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