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On arithmetic families of filtered $\varphi $-modules and crystalline representations

Part of: Discontinuous groups and automorphic forms Arithmetic problems. Diophantine geometry Families, fibrations

Published online by Cambridge University Press:  19 September 2012

Eugen Hellmann
Eugen Hellmann*
Affiliation:
Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany (hellmann@math.uni-bonn.de)
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Abstract

We consider stacks of filtered $\varphi $-modules over rigid analytic spaces and adic spaces. We show that these modules parameterize $p$-adic Galois representations of the absolute Galois group of a $p$-adic field with varying coefficients over an open substack containing all classical points. Further, we study a period morphism (defined by Pappas and Rapoport) from a stack parameterizing integral data, and determine the image of this morphism.

Keywords

Galois representationsp-adic Hodge theory

MSC classification

Secondary: 11F80: Galois representations 11F85: $p$-adic theory, local fields 14D23: Stacks and moduli problems 14G22: Rigid analytic geometry
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 12 , Issue 4 , October 2013 , pp. 677 - 726
Copyright
©Cambridge University Press 2012 

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