A counterexample to DG version of Han's conjecture
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918248344190976 |
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| author | Liu, Yeqin Shen, Yu |
| author_facet | Liu, Yeqin Shen, Yu |
| contents | In 2004, Han proposed the following conjecture: let $B$ be a finite-dimensional $k$-algebra. If $\mathrm{HH}_{n}(B)\neq 0$ for only finitely many $n\in \mathbb{Z}$, then $B$ is smooth. This conjecture can be generalized to the DG setting: let $B$ be a finite-dimensional DG $k$-algebra. If $\mathrm{HH}_{n}(B)\neq 0$ for only finitely many $n\in \mathbb{Z}$, then $B$ is smooth. In this note, we show that the DG generalization of Han's conjecture is false. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_12460 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A counterexample to DG version of Han's conjecture Liu, Yeqin Shen, Yu Rings and Algebras Algebraic Geometry K-Theory and Homology 16E10, 16E40, 16E45, 14F08 In 2004, Han proposed the following conjecture: let $B$ be a finite-dimensional $k$-algebra. If $\mathrm{HH}_{n}(B)\neq 0$ for only finitely many $n\in \mathbb{Z}$, then $B$ is smooth. This conjecture can be generalized to the DG setting: let $B$ be a finite-dimensional DG $k$-algebra. If $\mathrm{HH}_{n}(B)\neq 0$ for only finitely many $n\in \mathbb{Z}$, then $B$ is smooth. In this note, we show that the DG generalization of Han's conjecture is false. |
| title | A counterexample to DG version of Han's conjecture |
| topic | Rings and Algebras Algebraic Geometry K-Theory and Homology 16E10, 16E40, 16E45, 14F08 |
| url | https://arxiv.org/abs/2512.12460 |