Some topological aspects of a general spectra construction of Matsui and Takahashi
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912247471669248 |
|---|---|
| author | Yu, Xuan |
| author_facet | Yu, Xuan |
| contents | Matsui and Takahashi introduce a general spectra construction for triangulated categories in [J. Math. Soc. Japan, 4:2121-2150,2020], which is later used to establish Matsui's theory of triangular geometry. In this paper, we study several topological aspects of this general construction and give criteria for soberness and spectralness of the spectra. Furthermore, we discuss and generalize the immersion phenomenon for Noetherian schemes as appeared in [Pacific. J. Math., 313(2):433-457, 2021]. The last section illustrates that similar immersions also appear if the underlying category has a well-defined finite group action. We work in the extriangulated context to incorporate similar ideas from the triangulated and abelian contexts. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_18784 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Some topological aspects of a general spectra construction of Matsui and Takahashi Yu, Xuan Category Theory Commutative Algebra Algebraic Geometry Matsui and Takahashi introduce a general spectra construction for triangulated categories in [J. Math. Soc. Japan, 4:2121-2150,2020], which is later used to establish Matsui's theory of triangular geometry. In this paper, we study several topological aspects of this general construction and give criteria for soberness and spectralness of the spectra. Furthermore, we discuss and generalize the immersion phenomenon for Noetherian schemes as appeared in [Pacific. J. Math., 313(2):433-457, 2021]. The last section illustrates that similar immersions also appear if the underlying category has a well-defined finite group action. We work in the extriangulated context to incorporate similar ideas from the triangulated and abelian contexts. |
| title | Some topological aspects of a general spectra construction of Matsui and Takahashi |
| topic | Category Theory Commutative Algebra Algebraic Geometry |
| url | https://arxiv.org/abs/2502.18784 |