MAZUR'S INEQUALITY AND LAFFAILLE'S THEOREM

Christophe Cornut (1)

1 IMJ - Institut de Mathématiques de Jussieu

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.

Mots clés: Filtered G-isocrystals; Mazur's inequality; Harder-Narasimhan filtrations; tensor products

Domaines: Théorie des nombres [math.NT]

Christophe Cornut. MAZUR'S INEQUALITY AND LAFFAILLE'S THEOREM. 2015. ⟨hal-01188882v1⟩