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ϕ-modules

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

Slope filtrations in families
Ruochuan Liu
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 12 / Issue 2 / April 2013

Published online by Cambridge University Press:

17 May 2012, pp. 249-296

Print publication:

April 2013
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This paper concerns arithmetic families of $\varphi $-modules over reduced affinoid spaces. For such a family, we first prove that the slope polygons are lower semicontinuous around any rigid point. We further prove that if the slope polygons are locally constant around a rigid point, then around this point, the family has a global slope filtration after base change to some extended Robba ring.