Classifying subcategories of a Grothendieck category via its spectral category
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2026
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911736046551040 |
|---|---|
| author | Sazeedeh, Reza |
| author_facet | Sazeedeh, Reza |
| contents | Let $\mathcal{A}$ be a Grothendieck category. In this paper we classify subcategories of $\mathcal{A}$ via a support notion defined by Krause \cite{Kr2024} based on the spectral category of $\mathcal{A}$. We show that this aligns with Nemman's support \cite{Ne1992}, and thereby extends earlier classifications of subcategories of the category of modules over a commutative noetherian ring and subcategories of its derived category. Over a locally coherent category $\mathcal{A}$, we show that this support agrees with open subsets of the Ziegler topology on $\mathcal{A}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2606_00908 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Classifying subcategories of a Grothendieck category via its spectral category Sazeedeh, Reza Representation Theory 18E10, 18E35, 18E40 Let $\mathcal{A}$ be a Grothendieck category. In this paper we classify subcategories of $\mathcal{A}$ via a support notion defined by Krause \cite{Kr2024} based on the spectral category of $\mathcal{A}$. We show that this aligns with Nemman's support \cite{Ne1992}, and thereby extends earlier classifications of subcategories of the category of modules over a commutative noetherian ring and subcategories of its derived category. Over a locally coherent category $\mathcal{A}$, we show that this support agrees with open subsets of the Ziegler topology on $\mathcal{A}$. |
| title | Classifying subcategories of a Grothendieck category via its spectral category |
| topic | Representation Theory 18E10, 18E35, 18E40 |
| url | https://arxiv.org/abs/2606.00908 |