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

Published online by Cambridge University Press:  19 September 2012

Eugen Hellmann*
Mathematisches Institut der Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany (


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.

Research Article
©Cambridge University Press 2012 

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