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arXiv · 2008.09060

Bounding ramification by covers and curves

Hélène Esnault·Vasudevan Srinivas
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Abstract

We prove that $\bar {\mathbb Q}_\ell$-local systems of bounded rank and ramification on a smooth variety $X$ defined over an algebraically closed field $k$ of characteristic $p\neq \ell$ are tamified outside of codimension $2$ by a finite separable cover of bounded degree. In rank one, there is a curve which preserves their monodromy. There is a curve defined over the algebraic closure of a purely transcendental extension of $k$ of finite degree which fulfills the Lefschetz theorem. Last version: minor typos corrected.

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Hélène Esnault, Vasudevan Srinivas. 2020-08-20. Bounding ramification by covers and curves. https://arxiv.org/abs/2008.09060

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