Vol. 15, No. 9, 2021

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Reconstructing function fields from Milnor K-theory

Anna Cadoret and Alena Pirutka

Vol. 15 (2021), No. 9, 2261–2288
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 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 KM(F) determines the isomorphism class of F, when k is algebraically closed or finite.

Keywords
Milnor K-theory, function fields, reconstruction
Mathematical Subject Classification
Primary: 11R58, 14C35, 19D45
Milestones
Received: 11 April 2020
Revised: 11 January 2021
Accepted: 17 February 2021
Published: 23 December 2021
Authors
Anna Cadoret
Institut de Mathématiques de Jussieu–Paris Rive Gauche
Sorbonne Université
Paris
France
Alena Pirutka
Courant Institute of Mathematical Sciences
New York University
New York, NY
United States
National Research University Higher School of Economics
Moscow, Russia