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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Accesso online: | https://arxiv.org/abs/2405.06475 |
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| _version_ | 1866912335647473664 |
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| author | Modoi, George Ciprian |
| author_facet | Modoi, George Ciprian |
| contents | In this paper, we deal with two types of representability. The first is a variant of the Brown representability theorem in the spirit of Rouquier and Neeman. The second is a variant of the Brown-Adams representability. If $A$ is a dg-algebra over a commutative noetherian ring $R$, such that $A$ has coherent cohomology, it is shown that every cohomological (contravariant) functor $M:\mathbf{D}_{perf}(A)\to\mathrm{Mod}\textrm{-}R$, also satisfying $M(A[-n])\in\mathrm{mod}\textrm{-}R$, for all $n\in\mathbb{Z}$ is isomorphic to $\mathbf{D}(A)(-,X)|_{\mathbf{D}_{perf}(A)}$, where $X\in\mathbf{D}(A)$ is such that $H^n(X)$ is coherent for all $n\in\mathbb{Z}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_06475 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Brown--Adams representability for triangulated categories with locally coherent cohomology Modoi, George Ciprian Category Theory 18G80, 18G35 In this paper, we deal with two types of representability. The first is a variant of the Brown representability theorem in the spirit of Rouquier and Neeman. The second is a variant of the Brown-Adams representability. If $A$ is a dg-algebra over a commutative noetherian ring $R$, such that $A$ has coherent cohomology, it is shown that every cohomological (contravariant) functor $M:\mathbf{D}_{perf}(A)\to\mathrm{Mod}\textrm{-}R$, also satisfying $M(A[-n])\in\mathrm{mod}\textrm{-}R$, for all $n\in\mathbb{Z}$ is isomorphic to $\mathbf{D}(A)(-,X)|_{\mathbf{D}_{perf}(A)}$, where $X\in\mathbf{D}(A)$ is such that $H^n(X)$ is coherent for all $n\in\mathbb{Z}$. |
| title | Brown--Adams representability for triangulated categories with locally coherent cohomology |
| topic | Category Theory 18G80, 18G35 |
| url | https://arxiv.org/abs/2405.06475 |