Mazur's inequality and laffaille's theorem
Number Theory
2019-10-30 v2
Abstract
We look at various questions related to filtrations in -adic Hodgetheory, using a blend of building and Tannakian tools. Specifically,Fontaine and Rapoport used a theorem of Laffaille on filtered isocrystalsto establish a converse of Mazur's inequality for isocrystals. Wegeneralize both results to the setting of (filtered) -isocrystalsand also establish an analog of Totaro's -product theoremfor the Harder-Narasimhan filtration of Fargues.
Cite
@article{arxiv.1509.00574,
title = {Mazur's inequality and laffaille's theorem},
author = {Christophe Cornut},
journal= {arXiv preprint arXiv:1509.00574},
year = {2019}
}