English

Reocurrence and weak approximation over geometric global fields

Number Theory 2023-10-05 v1 Algebraic Geometry

Abstract

In this article, we prove a Reocurrence Theorem over function fields of curves over C( ⁣(t) ⁣)\mathbf{C}(\! (t)\! ) and over finite extensions of the Laurent series field C( ⁣(x,y) ⁣)\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 SLn\mathrm{SL}_n and with finite stabilizers is given at the end of the article.

Keywords

Cite

@article{arxiv.2310.02788,
  title  = {Reocurrence and weak approximation over geometric global fields},
  author = {Felipe Gambardella},
  journal= {arXiv preprint arXiv:2310.02788},
  year   = {2023}
}
R2 v1 2026-06-28T12:40:23.816Z