Vol. 11, No. 9, 2017

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Elementary equivalence versus isomorphism, II

Florian Pop

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

In this note we give sentences ${\vartheta }_{K}$ in the language of fields which describe the isomorphy type of $K$ among finitely generated fields, provided the Kronecker dimension $dim\left(K\right)$ satisfies $dim\left(K\right)<3$. 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