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arXiv · 1908.08291

\'Etale cohomology of rank one $\ell$-adic local systems in positive characteristic

Hélène Esnault·Moritz Kerz
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Abstract

We show that in positive characteristic special loci of deformation spaces of rank one $\ell$-adic local systems are quasilinear. From this we deduce the Hard Lefschetz theorem for rank one $\ell$-adic local systems and a generic vanishing theorem. Last version: a few typos corrected

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Hélène Esnault, Moritz Kerz. 2019-08-22. \'Etale cohomology of rank one $\ell$-adic local systems in positive characteristic. https://arxiv.org/abs/1908.08291

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