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arXiv · 2502.12075

A counterexample to the Jordan-H\"older property for polarizable semiorthogonal decompositions

Fabian Haiden·Dongjian Wu
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Abstract

We show that the Jordan-H\"older property fails for polarizable semiorthogonal decompositions -- those where every factor admits a Bridgeland stability condition. Counterexamples exist among Fukaya categories of surfaces and bounded derived categories of smooth projective varieties. Furthermore, we give an example of a smooth and proper pre-triangulated dg category with positive rank Grothendieck group which does not admit a stability condition.

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BibTeXRIS

Fabian Haiden, Dongjian Wu. 2025-02-17. A counterexample to the Jordan-H\"older property for polarizable semiorthogonal decompositions. https://arxiv.org/abs/2502.12075

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