Slope filtrations in families

Ruochuan Liu

doi:10.1017/S1474748012000709

Slope filtrations in families

Published online by Cambridge University Press: 17 May 2012

Ruochuan Liu

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Ruochuan Liu*: Affiliation:
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, USA ([email protected])

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Abstract

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.

Keywords

slope filtration ϕ-modules

Type: Research Article
Information: Journal of the Institute of Mathematics of Jussieu , Volume 12 , Issue 2 , April 2013 , pp. 249 - 296

DOI: https://doi.org/10.1017/S1474748012000709 [Opens in a new window]
Copyright: ©Cambridge University Press 2012

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