Characterizing finitely generated fields by a single field axiom

Publikation: Beitrag in FachzeitschriftForschungsartikelBeigetragenBegutachtung

Beitragende

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

OriginalspracheEnglisch
Seiten (von - bis)1203-1227
Seitenumfang25
FachzeitschriftAnnals of Mathematics
Jahrgang198
Ausgabenummer3
PublikationsstatusVeröffentlicht - 1 Nov. 2023
Peer-Review-StatusJa

Externe IDs

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

Schlagworte

ASJC Scopus Sachgebiete

Schlagwörter

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