Metric completions of triangulated categories from hereditary rings
Fuente:
arXiv
Salvato in:
| Autore principale: | |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917225454108672 |
|---|---|
| author | Matoušek, Cyril |
| author_facet | Matoušek, Cyril |
| contents | The focus of this article is on metric completions of triangulated categories arising in the representation theory of hereditary finite dimensional algebras and commutative rings. We explicitly describe all completions of bounded derived categories with respect to additive good metrics for two classes of rings - hereditary commutative noetherian rings and hereditary algebras of tame representation type over an algebraically closed field. To that end, we develop and study the lattice theory of metrics on triangulated categories. Moreover, we establish a link between metric completions of bounded derived categories of a ring and the ring's universal localisations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_20283 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Metric completions of triangulated categories from hereditary rings Matoušek, Cyril Representation Theory Commutative Algebra Category Theory 18G80 (Primary) 13D09, 16E35, 16G10 (Secondary) The focus of this article is on metric completions of triangulated categories arising in the representation theory of hereditary finite dimensional algebras and commutative rings. We explicitly describe all completions of bounded derived categories with respect to additive good metrics for two classes of rings - hereditary commutative noetherian rings and hereditary algebras of tame representation type over an algebraically closed field. To that end, we develop and study the lattice theory of metrics on triangulated categories. Moreover, we establish a link between metric completions of bounded derived categories of a ring and the ring's universal localisations. |
| title | Metric completions of triangulated categories from hereditary rings |
| topic | Representation Theory Commutative Algebra Category Theory 18G80 (Primary) 13D09, 16E35, 16G10 (Secondary) |
| url | https://arxiv.org/abs/2508.20283 |