Peterzil's trichotomy conjecture for o-minimal relics
Peterzil's trichotomy conjecture for o-minimal relics
Let be an o-minimal expansion of a real closed field, and let be a non-locally modular strongly minimal -relic, meaning a strongly minimal structure whose definable sets are interpretable in . Here denotes the algebraically closed field obtained by adjoining a square root of to the real closed field . Peterzil's conjecture. The structure interprets a copy of the algebraically closed field . This is a restricted version of Zilber's trichotomy conjecture for strongly minimal structures interpreted in o-minimal structures; the source presents it as a conjecture posed by Peterzil, and no resolution is supplied here.
Sources & referencesView supporting material
Primary source
Benjamin Castle, “The O-minimal Zilber Conjecture in Higher Dimensions”, arXiv:2406.09285 (2024).
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