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Donovan's Conjecture over Algebraically Closed Fields

OpenAI · September 24, 2026

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Abstract

We prove Donovan's conjecture over every algebraically closed field K of characteristic p > 0. For each fixed K and bound on defect-group order, blocks of finite groups represent only finitely many K-linear Morita equivalence classes. The defect groups need not be abelian, and the result includes p = 2.

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Collected automatically by AI tools (Claude Opus 5.5 and GPT-6 Astra, 2026-10-21) and not checked by a person. May be wrong or incomplete. Report an error.

Possibly relevant literature (found by the agent, not checked)

Charles W. Eaton and Michael Livesey, Donovan's conjecture and extensions by the centralizer of a defect group (arXiv:2006.11173, 2020-06-19). Gives a reduction of Donovan's conjecture through normal subgroups $N$ with $G = C_D(D \cap N)N$, with nonabelian applications ($Q_8 \times C_{2^n}$, $Q_8 \times Q_8$); this bears on the paper's passage from quasisimple base blocks to arbitrary groups via crossed extensions, and it is not in the paper's bibliography.

Elsewhere

VibeMathed: Problem record
Emergent Mind: family 203

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Cite

@misc{OAI:Donovans-Conjecture-over-Algebraic-Closures-of-Prime-Fields-September-24-2026,
  author = {{OpenAI}},
  title = {{Donovan's Conjecture over Algebraically Closed Fields}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Donovans-Conjecture-over-Algebraic-Closures-of-Prime-Fields-September-24-2026/main.pdf}{OAI:Donovans-Conjecture-over-Algebraic-Closures-of-Prime-Fields-September-24-2026}},
  year = {2026}
}