The correspondence between silting objects and $t$-structures for non-positive dg algebras
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arXiv
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| Formato: | Preprint |
| Publicado: |
2023
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| _version_ | 1866917879135338496 |
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| author | Fushimi, Riku |
| author_facet | Fushimi, Riku |
| contents | We establish a bijective correspondence between isomorphism classes of basic silting objects of $\mathsf{per}(A)$ and algebraic $t$-structures of $\mathsf{D}_{\rm fd}(A)$ for locally finite non-positive dg algebra $A$ over a field $k$ (more generally, we work in the setting of ST-pair inside an algebraic triangulated category). For a non-positive (topologically) homologically smooth dg $k$-algebra $A$ whose zeroth cohomology is finite-dimensional, or for a non-positive proper dg $k$-algebra $A$, the one-to-one correspondence between isomorphism classes of basic silting objects of $\mathsf{per}(A)$ and algebraic $t$-structures on $\mathsf{D}_{\rm fd}(A)$ was already known. The main result of this paper generalizes the above two results to locally finite non-positive dg $k$-algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17597 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The correspondence between silting objects and $t$-structures for non-positive dg algebras Fushimi, Riku Representation Theory 16E35, 16E45, 18G80 We establish a bijective correspondence between isomorphism classes of basic silting objects of $\mathsf{per}(A)$ and algebraic $t$-structures of $\mathsf{D}_{\rm fd}(A)$ for locally finite non-positive dg algebra $A$ over a field $k$ (more generally, we work in the setting of ST-pair inside an algebraic triangulated category). For a non-positive (topologically) homologically smooth dg $k$-algebra $A$ whose zeroth cohomology is finite-dimensional, or for a non-positive proper dg $k$-algebra $A$, the one-to-one correspondence between isomorphism classes of basic silting objects of $\mathsf{per}(A)$ and algebraic $t$-structures on $\mathsf{D}_{\rm fd}(A)$ was already known. The main result of this paper generalizes the above two results to locally finite non-positive dg $k$-algebras. |
| title | The correspondence between silting objects and $t$-structures for non-positive dg algebras |
| topic | Representation Theory 16E35, 16E45, 18G80 |
| url | https://arxiv.org/abs/2312.17597 |