Rickard's question on standard derived equivalences

Wei Hu, Changchang Xi, Jin Zhang

arXiv:2608.09062v1 Primary: math.RT Secondary: math.RA

Abstract

In 1991 Rickard asked whether every derived equivalence of algebras over a common field is standard. We construct a series of examples of non-standard derived equivalences, and thus answer the question negatively. Moreover, we give a necessary and sufficient condition for the question to be true.

Disclosure

“l- ogy in August 2026, a preliminary version of the work was completed. Xi is very grateful to Professor Zhicheng Feng for his invitation and warm hospitality. When considering the proof of Lemma 4.3 in the case A = k[x]/(x3 ), we asked ChatGPT Pro for help. It suggested a similar condition. References [1] K. K. Arnesen, R. Laking, D. Pauksztello, Morphisms between indecomposable complexes in the bounded derived catego”
PDF page 20

Classification: Proof ideas or individual proof-step assistance
Multiplier: 8
Verified: 2026-08-23T05:07:11.043502Z

Structural counts

Pages 21 pdf

Theorems 3 source

Lemmas 7 source

Propositions 4 source

Corollaries 0 source

Definitions 1 source

Displayed equations 86 source

Bibliography entries 16 source

Appendix pages 0 estimated

Count notes

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