Harder-Narasimhan categories
Huayi Chen (CMLS-EcolePolytechnique)

TL;DR
This paper introduces arithmetic exact categories, generalizing Quillen's exact categories, and develops a framework for Harder-Narasimhan filtrations and polygons with functorial properties, extending classical formalism.
Contribution
It proposes a new class of categories called arithmetic exact categories and establishes conditions for defining Harder-Narasimhan filtrations and polygons within them, including their functoriality.
Findings
Defined arithmetic exact categories as a generalization of Quillen's exact categories.
Established conditions for Harder-Narasimhan filtrations and polygons in these categories.
Proved the functoriality of Harder-Narasimhan filtrations indexed by real numbers.
Abstract
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 ), which can not be stated in the classical setting of Harder and Narasimhan's formalism.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory
