Harder-Narasimhan categories

Huayi Chen (1)

1 CMLS - Centre de Mathématiques Laurent Schwartz

We propose a generalization of Quillen's exact category --- arithmetic exact category and we discuss conditions on such categories under which one can establish the notion of Harder-Narasimhan filtrations and Harder-Narsimhan polygons. Furthermore, we show the functoriality of Harder-Narasimhan filtrations (indexed by $\mathbb R$), which can not be stated in the classical setting of Harder and Narasimhan's formalism.

Mots clés: category; Harder-Narasimhan filtration; Harder-Narasimhan measure

Domaines: Géométrie algébrique [math.AG]; Catégories et ensembles [math.CT]

Huayi Chen. Harder-Narasimhan categories. Journal of Pure and Applied Algebra, 2010, 214 (2), pp.187-200. ⟨10.1016/j.jpaa.2009.05.009⟩. ⟨hal-00155665v2⟩