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Donovan's conjecture on Morita finiteness of blocks with a given defect group

Field paper, Theorem 1.1: for each prime $p$ , algebraically closed $K$ of characteristic $p$ and bound $M$ , blocks of finite groups over $K$ with defect groups of order at most $M$ represent only finitely many $K$ -linear Morita classes; defect groups may be nonabelian and $p=2$ is included. Integral companion, Theorem 1.1 and Corollary: the same over $W(\overline{\mathbb F}_p)$ and over each fixed complete DVR of characteristic zero with algebraically closed residue field, ramified included. Consequences: bounded Cartan entries and Loewy lengths. Not shown: explicit lists or bounds on the number of classes, or Morita finiteness over coefficient fields that are not algebraically closed.

Exact FrontierDelta

Prior state unknown→proved

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Occurred: Sep 24, 2026

Delta type: SOURCE CLAIM

Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.

Canonical aliases: Donovan's conjecture on Morita finiteness of blocks with a given defect group · Donovan's conjecture

Confidence: Not scored

Registry verification: unreviewed · announcement · candidate

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Unreleased internal OpenAI model
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VibeMathed record: Donovan's conjecture on Morita finiteness of blocks with a given defect group

specialist registry · passed

No independent mathematician has checked this yet. Checked here: abstracts, introductions and main theorems of both manuscripts (TeX source), read against Donovan's conjecture as recorded by Alperin. The field paper's Theorem 1.1 is the bounded-defect-order form over every algebraically closed field of characteristic $p$ (equivalent to the fixed-defect-group form, as the paper notes); the companion's Theorem 1.1 gives the integral form over $W(\overline{\mathbb F}_p)$ and a corollary over every fixed complete characteristic-zero DVR with algebraically closed residue field. The field paper says its proof is independent of the integral companion, but its final coefficient-extension step recalls an argument from another unreviewed release manuscript (The Blockwise Alperin Weight Conjecture, Section 2.1). The proofs were not refereed. No Lean formalization.

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Donovan's conjecture on Morita finiteness of blocks with a given defect group

witness · pending

Primary source named by the VibeMathed record. Presence in this import is not an independent mathematical verification.

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Integral Donovan Finiteness over Witt Vectors (companion)

paper · pending

paper link supplied by the VibeMathed registry.

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Donovan's conjecture on Morita finiteness of blocks with a given defect group evidence for this event

Integral Donovan Finiteness over Witt Vectors (companion) evidence for this event

VibeMathed record: Donovan's conjecture on Morita finiteness of blocks with a given defect group evidence for this event

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