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arXiv · 2602.16398

Effective local differential topology of algebraic varieties over local fields of positive characteristics

Avraham Aizenbud·Dmitry Gourevitch·David Kazhdan·Eitan Sayag
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Abstract

In this paper we provide a framework for quantitative statements on distances and measures when studying algebraic varieties and morphisms of algebraic varieties over local fields. We will concentrate on local fields of the type $\mathbb{F}_\ell((t))$ and work uniformly with respect to finite extensions of $\mathbb{F}_\ell$. In this framework we prove analogues of standard results from local differential topology, including the implicit function theorem and study the behavior of smooth measures under push forward with respect to submersions.

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Avraham Aizenbud, Dmitry Gourevitch, David Kazhdan, Eitan Sayag. 2026-02-18. Effective local differential topology of algebraic varieties over local fields of positive characteristics. https://arxiv.org/abs/2602.16398

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