A $p$-adic Bertini theorem for unipotent local systems

Christopher Lazda

A $p$-adic Bertini theorem for unipotent local systems

Number Theory 2013-11-26 v3

Authors: Christopher Lazda

Abstract

In this short note we prove a version of Bertini's theorem for unipotent rigid fundamental groups, stating that for every smooth, projective, geometrically connected variety $X$ over an infinite perfect field $k$ of characteristic $p>0$ , there exists a smooth, projective, geometrically connected curve $C\subset X$ such that the induced map on rigid fundamental groups is surjective.

Keywords

algebraic varieties projective varieties mapping class groups

Cite

@article{arxiv.1301.6073,
  title  = {A $p$-adic Bertini theorem for unipotent local systems},
  author = {Christopher Lazda},
  journal= {arXiv preprint arXiv:1301.6073},
  year   = {2013}
}

Comments

This paper has been withdrawn as it was pointed out by a referee that the main theorem follows easily from the weak Lefschetz theorem

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