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Vanishing Cycles for Zariski-Constructible Sheaves on Rigid Analytic Varieties (2504.16365v1)
Published 23 Apr 2025 in math.AG
Abstract: We develop a theory of nearby and vanishing cycles in the context of finite-coefficient Zariski-constructible sheaves over a non-archimedean field which is non-trivially valued, complete, algebraically closed, and of mixed characteristic or equal characteristic zero. Apart from basic properties, we show that they preserve Zariski-constructibility, have a Milnor fibre interpretation, satisfy Beilinson's gluing construction, are perverse t-exact, and commute with Verdier duality.
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