Characterizing finitely generated fields by a single field axiom
Research output: Contribution to journal › Research article › Contributed › peer-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 language | English |
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Pages (from-to) | 1203-1227 |
Number of pages | 25 |
Journal | Annals of Mathematics |
Volume | 198 |
Issue number | 3 |
Publication status | Published - 1 Nov 2023 |
Peer-reviewed | Yes |
External IDs
Mendeley | d8c7187b-b4b2-3983-999f-e30618c9f0e0 |
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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