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Mazur’s inequality and Laffaille’s theorem. (English) Zbl 07087162
Summary: 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.

14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
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