Nearby and vanishing cycle functors on rigid analytic varieties preserve Zariski-constructibility, satisfy Beilinson gluing, are perverse t-exact, and commute with Verdier duality.
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Vanishing Cycles for Zariski-Constructible Sheaves on Rigid Analytic Varieties
Nearby and vanishing cycle functors on rigid analytic varieties preserve Zariski-constructibility, satisfy Beilinson gluing, are perverse t-exact, and commute with Verdier duality.