Elementary equivalence versus isomorphism, II

Pop, Florian

doi:10.2140/ant.2017.11.2091

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Elementary equivalence versus isomorphism, II

Florian Pop

Vol. 11 (2017), No. 9, 2091–2111

DOI: 10.2140/ant.2017.11.2091

Abstract

In this note we give sentences $ϑ_{K}$ 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

Vol. 11, No. 9, 2017