Characterizing finitely generated fields by a single field axiom

Research output: Contribution to journalResearch articleContributedpeer-review

Contributors

Abstract

We resolve the strong Elementary Equivalence versus Isomorphism Problem for finitely generated fields. That is, we show that for every field in this class there is a first-order sentence which characterizes this field within the class up to isomorphism. Our solution is conditional on resolution of singularities in characteristic two and unconditional in all other characteristics.

Details

Original languageEnglish
Pages (from-to)1203-1227
Number of pages25
JournalAnnals of Mathematics
Volume198
Issue number3
Publication statusPublished - 1 Nov 2023
Peer-reviewedYes

External IDs

Mendeley d8c7187b-b4b2-3983-999f-e30618c9f0e0
Scopus 85177841388

Keywords

ASJC Scopus subject areas

Keywords

  • Pfister forms, elementary equivalence versus isomorphism, finitely generated fields, firstorder definability of valuations, higher-dimensional cohomological local-global principles