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arXiv · 2512.12460

A counterexample to DG version of Han's conjecture

Yeqin Liu·Yu Shen
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Abstract

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.

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Yeqin Liu, Yu Shen. 2025-12-13. A counterexample to DG version of Han's conjecture. https://arxiv.org/abs/2512.12460

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