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Article Dans Une Revue Mathematische Annalen Année : 2019

MAZUR'S INEQUALITY AND LAFFAILLE'S THEOREM

Résumé

We look at various questions related to filtrations in $p$-adic Hodge theory, using a blend of building and Tannakian tools. Specifically, Fontaine and Rapoport used a theorem of Laffaille on filtered isocrystals to establish a converse of Mazur's inequality for isocrystals. We generalize both results to the setting of (filtered) $G$-isocrystals and also establish an analog of Totaro's $\otimes$-product theorem for the Harder-Narasimhan filtration of Fargues.
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Dates et versions

hal-01188882 , version 1 (31-08-2015)
hal-01188882 , version 2 (28-10-2019)

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Christophe Cornut. MAZUR'S INEQUALITY AND LAFFAILLE'S THEOREM. Mathematische Annalen, 2019, 374 (3-4), pp.1657-1679. ⟨10.1007/s00208-018-1788-3⟩. ⟨hal-01188882v2⟩
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