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Cohomology of arithmetic families of $ (\varphi, \Gamma)$-modules


Authors: Kiran S. Kedlaya, Jonathan Pottharst and Liang Xiao
Journal: J. Amer. Math. Soc. 27 (2014), 1043-1115
MSC (2010): Primary 11F33, 11R23, 11S25, 11S31
DOI: https://doi.org/10.1090/S0894-0347-2014-00794-3
Published electronically: April 3, 2014
MathSciNet review: 3230818
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Abstract: We prove the finiteness and compatibility with base change of the $ (\varphi , \Gamma )$-cohomology and the Iwasawa cohomology of arithmetic families of $ (\varphi , \Gamma )$-modules. Using this finiteness theorem, we show that a family of Galois representations that is densely pointwise refined in the sense of Mazur is actually trianguline as a family over a large subspace. In the case of the Coleman-Mazur eigencurve, we determine the behavior at all points.


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Additional Information

Kiran S. Kedlaya
Affiliation: Department of Mathematics, University of California, San Diego, La Jolla, California 92093
Email: kedlaya@ucsd.edu

Jonathan Pottharst
Affiliation: 5 Redwood Street, Boston, Massachusetts 02122
Email: jay@vbrt.org

Liang Xiao
Affiliation: Department of Mathematics, University of California, Irvine, Rowland Hall 340, Irvine, California 92697
Email: lxiao@math.uci.edu

DOI: https://doi.org/10.1090/S0894-0347-2014-00794-3
Received by editor(s): June 26, 2012
Received by editor(s) in revised form: August 14, 2013
Published electronically: April 3, 2014
Article copyright: © Copyright 2014 by Kiran S. Kedlaya, Jonathan Pottharst, and Liang Xiao

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