On Harder-Narasimhan filtrations and their compatibility with tensor products

Sur les filtrations de Harder-Narasimhan et leur compatibilité avec le produit tensoriel

Christophe Cornut (1)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche

We attach buildings to modular lattices and use them to develop a metric approach to Harder-Narasimhan filtrations. Switching back to a categorical framework, we establish an abstract numerical criterion for the compatibility of these filtrations with tensor products. We finally verify our criterion in three cases, one of which is new.

Mots clés: Modular lattices; Quasi-Tannakian categories; Harder-Narasiman filtrations; Buildings

Domaines: Théorie des nombres [math.NT]; Géométrie métrique [math.MG]; Catégories et ensembles [math.CT]

Christophe Cornut. On Harder-Narasimhan filtrations and their compatibility with tensor products. Confluentes Mathematici, 2018, 10 (2), pp.3-49. ⟨10.5802/cml.49⟩. ⟨hal-01494169v2⟩