Peterzil's trichotomy conjecture for o-minimal relics

Let R\mathcal R be an o-minimal expansion of a real closed field, and let M\mathcal M be a non-locally modular strongly minimal R\mathcal R-relic, meaning a strongly minimal structure whose definable sets are interpretable in R\mathcal R. Here R[i]R[i] denotes the algebraically closed field obtained by adjoining a square root ii of 1-1 to the real closed field RR. Peterzil's conjecture. The structure M\mathcal M interprets a copy of the algebraically closed field R[i]R[i]. 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).

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.