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Variants of formal nearby cycles

Part of: Arithmetic problems. Diophantine geometry (Co)homology theory

Published online by Cambridge University Press:  19 August 2013

Yoichi Mieda
Yoichi Mieda*
Affiliation:
The Hakubi Center for Advanced Research/Department of Mathematics, Kyoto University, Kyoto, 606–8502, Japan (mieda@math.kyoto-u.ac.jp)
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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.

Keywords

nearby cycleétale cohomologyrigid geometry

MSC classification

Secondary: 14F20: Étale and other Grothendieck topologies and (co)homologies 14G20: Local ground fields 14G22: Rigid analytic geometry
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 13 , Issue 4 , October 2014 , pp. 701 - 752
Copyright
©Cambridge University Press 2013 

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