Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 

 

Comparison results for étale cohomology in rigid geometry


Author: Yoichi Mieda
Journal: J. Algebraic Geom. 23 (2014), 91-115
DOI: https://doi.org/10.1090/S1056-3911-2013-00607-4
Published electronically: September 9, 2013
MathSciNet review: 3121849
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Abstract | References | Additional Information

Abstract: We give some comparison results between étale cohomology of schemes and that of associated rigid spaces. First we work in the framework of Fujiwara spaces, and prove a comparison theorem for the derived direct image of morphisms which are not necessarily proper. We need the assumption that the base of the comparison functor consists of schemes of finite type over a field. Next, we consider an analogous problem for adic spaces. In this case, we can prove the comparison theorem under the condition that the base of the comparison functor consists of schemes of finite type over a complete discrete valuation ring with equal characteristic. Finally we propose a definition of the nearby cycle functor for an adic space over a complete discrete valuation ring and give a comparison result on it.


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Additional Information

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

DOI: https://doi.org/10.1090/S1056-3911-2013-00607-4
Received by editor(s): January 19, 2011
Received by editor(s) in revised form: June 6, 2011
Published electronically: September 9, 2013
Article copyright: © Copyright 2013 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.

Journal of Algebraic Geometry
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