Silting theory and derived base change
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866917353193734144 |
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| author | Fushimi, Riku |
| author_facet | Fushimi, Riku |
| contents | For finite-dimensional algebras over a field, Koenig and Yang established a bijection between silting complexes and simple-minded collections in the bounded derived category, with further contributions by many authors in various settings. In this paper, we work over a commutative complete local noetherian ring $(R,\m,k)$ rather than over a field and establish a bijection in this more general setting.
As an application of this generalization, we construct a bijection between silting complexes over a noetherian $R$-algebra $Λ$ and silting complexes over $Λ\ten^\LL_RS$ for any morphism of commutative complete local noetherian rings $(R,\m,k)\to(S,\n,k)$. This result generalizes some known results on silting complexes over noetherian algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_18790 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Silting theory and derived base change Fushimi, Riku Representation Theory 16E35, 16E45, 18G80 For finite-dimensional algebras over a field, Koenig and Yang established a bijection between silting complexes and simple-minded collections in the bounded derived category, with further contributions by many authors in various settings. In this paper, we work over a commutative complete local noetherian ring $(R,\m,k)$ rather than over a field and establish a bijection in this more general setting. As an application of this generalization, we construct a bijection between silting complexes over a noetherian $R$-algebra $Λ$ and silting complexes over $Λ\ten^\LL_RS$ for any morphism of commutative complete local noetherian rings $(R,\m,k)\to(S,\n,k)$. This result generalizes some known results on silting complexes over noetherian algebras. |
| title | Silting theory and derived base change |
| topic | Representation Theory 16E35, 16E45, 18G80 |
| url | https://arxiv.org/abs/2603.18790 |