OpenAI · 203-02 · 2026-09-25 · Algebra
Integral Donovan Finiteness over Witt Vectors
preprints/Integral-Donovan-Finiteness-over-Witt-Vectors-September-25-2026
Family 203. Donovan's conjecture over fields and discrete valuation rings.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Proves Donovan's conjecture: over each fixed algebraically closed field of characteristic , blocks of finite groups with bounded defect-group order have only finitely many Morita-equivalence classes, for every prime . Also proves the integral form over each fixed complete mixed-characteristic discrete valuation ring with algebraically closed residue field.
We prove integral Donovan finiteness: for every prime p and positive integer M, the blocks of all finite groups with defect groups of order at most M have only finitely many Morita equivalence classes over . The defect groups need not be abelian, and the result includes p = 2. The same bounded-defect finiteness holds over each fixed complete discrete valuation ring of characteristic zero with algebraically closed residue field of characteristic p, including ramified rings.
Preprint source and Lean scope
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No Lean scope note is in the repository for this family. The preprint source below is still the full manuscript, not only the abstract. No compilation is asserted.