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arXiv · 2310.02788

Reocurrence and weak approximation over geometric global fields

Felipe Gambardella
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Abstract

In this article, we prove a Reocurrence Theorem over function fields of curves over $\mathbf{C}(\! (t)\! )$ and over finite extensions of the Laurent series field $\mathbf{C}(\! (x,y)\! )$. This provides a partial replacement to Chebotarev's Theorem over such fields. A concrete application to the study of weak approximation for homogeneous spaces under $\mathrm{SL}_n$ and with finite stabilizers is given at the end of the article.

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Felipe Gambardella. 2023-10-04. Reocurrence and weak approximation over geometric global fields. https://arxiv.org/abs/2310.02788

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