Han's conjecture on Hochschild homology and smoothness
Let be a finite-dimensional algebra over an algebraically closed field . Write for the Hochschild homology groups of . The algebra is (homologically) smooth over when it is perfect as a bimodule over its enveloping algebra. Han's conjecture. If is nonzero for only finitely many , then is (homologically) smooth over . The conjecture is a classical statement for finite-dimensional algebras; this paper's abstract distinguishes it from the DG generalization, which the paper disproves. The supplied text does not state whether Han's original conjecture has been resolved.
References
Primary source
Yeqin Liu and Yu Shen, “A counterexample to DG version of Han's conjecture”, arXiv:2512.12460 (2025).
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