Vol. 15, No. 9, 2021

Download this article
Download this article For screen
For printing
Recent Issues

Volume 16
Issue 2, 231–519
Issue 1, 1–230

Volume 15, 10 issues

Volume 14, 10 issues

Volume 13, 10 issues

Volume 12, 10 issues

Volume 11, 10 issues

Volume 10, 10 issues

Volume 9, 10 issues

Volume 8, 10 issues

Volume 7, 10 issues

Volume 6, 8 issues

Volume 5, 8 issues

Volume 4, 8 issues

Volume 3, 8 issues

Volume 2, 8 issues

Volume 1, 4 issues

The Journal
About the Journal
Editorial Board
Editors’ Interests
Submission Guidelines
Submission Form
Policies for Authors
Ethics Statement
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Author Index
To Appear
Other MSP Journals
This article is available for purchase or by subscription. See below.
Reconstructing function fields from Milnor K-theory

Anna Cadoret and Alena Pirutka

Vol. 15 (2021), No. 9, 2261–2288

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.

PDF Access Denied

However, your active subscription may be available on Project Euclid at

We have not been able to recognize your IP address as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recom­mendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 40.00:

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