Variants of formal nearby cycles

Details Variants of formal nearby cycles Variants of formal nearby cycles

2010-05-31

arxiv.org/abs/1005.5616v2

Mathematics

Algebraic Geometry

38 pages

Scientific paper

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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