Submission date: 27 October 2023

Abstract:

Bakker, Brunebarbe, Tsimerman showed in [bakker2022minimal] that the definable structure sheaf 𝒪_{ℂ^n} of ℂ^n is a coherent 𝒪_{ℂ^n}-module as a sheaf on the site ℂ^n, where the coverings are finite coverings by definable open sets. In general, let 𝕂 be an algebraically closed field of characteristic zero. We give a more model-theoretic proof of the coherence of \mathcal{O}_{𝕂^n} as a sheaf of 𝒪_{𝕂^n}-module on the site 𝕂^n using spectral topology on the type space S_n(𝕂).

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Full text arXiv 2310.17862: pdf, ps.