تقرير
Length of triangulated categories
| العنوان: | Length of triangulated categories |
|---|---|
| المؤلفون: | Hirano, Yuki, Kalck, Martin, Ouchi, Genki |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Algebraic Geometry, Mathematics - Category Theory, Mathematics - Rings and Algebras, Mathematics - Representation Theory, 14F08, 18G80, 14H60 |
| الوصف: | We introduce the notion of composition series and the length of triangulated categories, and we study compositions series of derived categories of certain projective varieties and finite dimensional algebras. For example, we compute the length of the derived category ${\rm D}^{\rm b}(C)$ of a smooth projective curve $C$ and classify all finite length thick subcategories of ${\rm D}^{\rm b}(C)$. Furthermore, we prove that the derived categories of certain smooth projective varieties have composition series of different lengths. We also discuss the length of (1) derived categories of finite dimensional representations of Dynkin and extended Dynkin quivers, (2) derived categories of some singular varieties and (3) Krah's phantom subcategories. Comment: 40 pages. Major revision. New coauthor joined. Counterexamples to the Jordan--Dedekind property are added |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2404.07583 |
| رقم الأكسشن: | edsarx.2404.07583 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |