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

  title={{\'E}tale cohomology of rank one \$\$\ell \$\$-adic local systems in positive characteristic},
  author={H'elene Esnault and Moritz Kerz},
  journal={arXiv: Algebraic Geometry},
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. 
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