TL;DR
This paper introduces new variants of formal nearby cycles for formal schemes, generalizing existing concepts without rigid geometry, aimed at studying Rapoport-Zink space cohomology.
Contribution
It presents a scheme-theoretic construction of formal nearby cycles that generalizes Berkovich's approach, applicable to locally algebraizable formal schemes.
Findings
Provides a new scheme-theoretic framework for formal nearby cycles.
Generalizes Berkovich's formal nearby cycle for algebraizable schemes.
Aims to facilitate local cohomological analysis of Rapoport-Zink spaces.
Abstract
In this paper, we introduce variants of formal nearby cycles for a locally noetherian formal scheme over a complete discrete valuation ring. If the formal scheme is locally algebraizable, then our nearby cycle gives a generalization of Berkovich's formal nearby cycle. Our construction is entirely scheme-theoretic and does not require rigid geometry. Our theory is intended for applications to the local study of the cohomology of Rapoport-Zink spaces.
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