Elementary equivalence versus isomorphism, II

Florian Pop

doi:10.2140/ant.2017.11.2091

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Home > Journals > Algebra Number Theory > Volume 11 > Issue 9 > Article

2017 Elementary equivalence versus isomorphism, II

Florian Pop

Algebra Number Theory 11(9): 2091-2111 (2017). DOI: 10.2140/ant.2017.11.2091

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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).

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Florian Pop. "Elementary equivalence versus isomorphism, II." Algebra Number Theory 11 (9) 2091 - 2111, 2017. https://doi.org/10.2140/ant.2017.11.2091

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Received: 23 April 2016; Revised: 11 May 2017; Accepted: 3 August 2017; Published: 2017

First available in Project Euclid: 20 December 2017

zbMATH: 06818945

MathSciNet: MR3735462

Digital Object Identifier: 10.2140/ant.2017.11.2091

Subjects:

Primary: 11G30 , 14H25

Secondary: 03C62 , 11G99 , 12F20 , 12G10 , 12L12 , 13F30

Keywords: elementary equivalence versus isomorphism , finitely generated fields , first-order definability , Galois étale cohomology , Kato's higher local-global principles , Milnor $K$-groups

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