A-analyticity of separatrices of foliations

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发表日期：

2025年4月18日

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Stéphane Druel

摘要

Let X be a smooth quasi-projective surface over a number field K, and let L be a possibly singular foliation on X. Suppose that, for almost all non-zero prime ideal $\mathfrak {p}$ $p$ of the ring of integers R of K, the reduction of L modulo $\mathfrak {p}$ $p$ is closed under pth powers, where p denotes the characteristic of the residue field $R/\mathfrak {p}$ $R / p$ . Then any L-invariant smooth formal curve is A-analytic. Building on prior work of Bost we obtain an algebraicity criterion for those curves.