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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