Vanishing Cycles for Zariski-Constructible Sheaves on Rigid Analytic Varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917995588091904 |
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| author | Zhou, Tong |
| author_facet | Zhou, Tong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_16365 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Vanishing Cycles for Zariski-Constructible Sheaves on Rigid Analytic Varieties Zhou, Tong Algebraic Geometry 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. |
| title | Vanishing Cycles for Zariski-Constructible Sheaves on Rigid Analytic Varieties |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2504.16365 |