A new rigid-analytic theorem on Frobenius-invariant subsets of ℓ-adic character groups implies Hard Lefschetz and generic vanishing for rank one local systems in positive characteristic.
: Vanishing theorems for perverse sheaves on abelian varieties, revisited , Selecta Math
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\'Etale cohomology of rank one $\ell$-adic local systems in positive characteristic
A new rigid-analytic theorem on Frobenius-invariant subsets of ℓ-adic character groups implies Hard Lefschetz and generic vanishing for rank one local systems in positive characteristic.