Slope filtrations in families

Abstract

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

Final version

Cited by in corpus (2)

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