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Christophe Cornut
On Harder-Narasimhan filtrations and their compatibility with tensor products
Confluentes Mathematici, 10 no. 2 (2018), p. 3-49, doi: 10.5802/cml.49
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Class. Math.: 06C05, 51E24, 53C23, 18D10, 20G15
Mots clés: Harder-Narasimhan filtrations, Quasi-Tannakian categories

Résumé - Abstract

We attach buildings to modular lattices of finite length and show that they yield a natural framework for a metric version of the Harder-Narasimhan formalism. We establish a sufficient condition for the compatibility of Harder-Narasimhan filtrations with tensor products and verify our criterion in various cases coming from $p$-adic Hodge theory.

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