Phi-modules and coefficient spaces

Details Phi-modules and coefficient spaces Phi-modules and coefficient spaces

2008-11-07

arxiv.org/abs/0811.1170v1

Mathematics

Algebraic Geometry

41 pages

Scientific paper

We define and study certain moduli stacks of modules equipped with a Frobenius semi-linear endomorphism. These stacks can be thought of as parametrizing the coefficients of a variable Galois representation and are global variants of the spaces of Kisin-Breuil $\Phi$-modules used by Kisin in his study of deformation spaces of local Galois representations. We also define a version of a rigid analytic period map for these spaces, we show how their local structure can be described in terms of "local models", and we show how Bruhat-Tits buildings can be used to study their special fibers.

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