Harder-Narasimhan categories

Details Harder-Narasimhan categories Harder-Narasimhan categories

2007-06-18

arxiv.org/abs/0706.2648v2

Mathematics

Algebraic Geometry

Scientific paper

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.

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