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arXiv · 2504.16365

Vanishing Cycles for Zariski-Constructible Sheaves on Rigid Analytic Varieties

Tong Zhou
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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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Tong Zhou. 2025-04-23. Vanishing Cycles for Zariski-Constructible Sheaves on Rigid Analytic Varieties. https://arxiv.org/abs/2504.16365

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