Slope filtrations revisited

Abstract

We give a "second generation" exposition of the slope filtration theorem for modules with Frobenius action over the Robba ring, providing a number of simplifications in the arguments. Some of these are inspired by parallel work of Hartl and Pink, which points out some analogies with the formalism of stable vector bundles.

75 pages; v4: corrects minor errors in 4.3.5, 4.4.2, 6.3.1

References in corpus (4)

• Filtrations de type Hasse-Arf et monodromie p-adique
• Sur le théorème de l'indice des équations différentielles p-adiques. III
• Full faithfulness for overconvergent F-isocrystals
• The p-adic local monodromy theorem for fake annuli

Cited by in corpus (17)

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• Classification of two dimensional split trianguline representations of $p$-adic fields
• Slope filtrations for relative Frobenius
• p-adic families of Galois representations and higher rank Selmer groups
• Deformations of trianguline B-pairs and Zariski density of two dimensional crystalline representations
• A Dictionary between Fontaine-Theory and its Analogue in Equal Characteristic
• Semistable reduction for overconvergent F-isocrystals, IV: Local semistable reduction at nonmonomial valuations
• On period spaces for p-divisible groups
• Frobenius modules over multivariate Robba rings
• On the rationality and continuity of logarithmic growth filtration of solutions of $p$-adic differential equations
• On Families of (Phi,Gamma)-modules
• Swan conductors for p-adic differential modules, I: A local construction
• On differential modules associated to de Rham representations in the imperfect residue field case
• Harder-Narasimhan theory
• Derivatives of Frobenius and Derivatives of Hodge weights
• A group-theoretic generalization of the $p$-adic local monodromy theorem