A counterexample to Han's conjecture

Bochao Kong, Yeqin Liu, Yu Shen

arXiv:2608.00177v1 Primary: math.RA Secondary: math.AG

Abstract

There is a finite dimensional $\mathbb{C}$-algebra with $\mathrm{gldim}(A)=\infty$ and $\mathrm{HH}_{n}(A)=0$ for $n\geq 1$.

Disclosure

“proves the Hochschild-vanishing and infinite-global-dimension claims. Appendix A verifies the required compatibility on dg enhancements. 1.3. Acknowledgments The counterexample presented in this paper was discovered with the assistance of OpenAI’s GPT-5.6 Sol Ultra model. All mathematical arguments and references were independently verified by the authors. 1.4. Notations All algebras are unital and associative. All module categories and derived categories are formed using right modules unl”
PDF page 3

Classification: Substantial mathematical content or result generation
Multiplier: 10
Verified: 2026-08-23T19:17:34.402759Z

Structural counts

Pages 23 pdf

Theorems 3 source

Lemmas 7 source

Propositions 3 source

Corollaries 2 source

Definitions 0 source

Displayed equations 143 source

Bibliography entries 25 source

Appendix pages 13 estimated

Count notes

Source counts use the expanded primary TeX file draft6.tex.
Appendix pages include the first PDF page with an explicit Appendix heading through the final page.