Vol. 11, No. 9, 2017

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

Volume 12
Issue 5, 1001–1309
Issue 4, 751–999
Issue 3, 493–750
Issue 2, 227–492
Issue 1, 1–225

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
Subscriptions
Editorial Board
Editors' Addresses
Editors' Interests
Scientific Advantages
Submission Guidelines
Submission Form
Editorial Login
Author Index
To Appear
 
ISSN: 1944-7833 (e-only)
ISSN: 1937-0652 (print)
Elementary equivalence versus isomorphism, II

Florian Pop

Vol. 11 (2017), No. 9, 2091–2111
Abstract

In this note we give sentences ϑK in the language of fields which describe the isomorphy type of K among finitely generated fields, provided the Kronecker dimension dim(K) satisfies dim(K) < 3. This extends results by Rumely (1980) concerning global fields; see also Scanlon (2008).

Keywords
elementary equivalence versus isomorphism, first-order definability, finitely generated fields, Milnor $K$-groups, Galois étale cohomology, Kato's higher local-global principles
Mathematical Subject Classification 2010
Primary: 11G30, 14H25
Secondary: 03C62, 11G99, 12F20, 12G10, 12L12, 13F30
Milestones
Received: 23 April 2016
Revised: 11 May 2017
Accepted: 3 August 2017
Published: 2 December 2017
Authors
Florian Pop
Department of Mathematics
University of Pennsylvania
Philadelphia, PA
United States