{"id":"openai-math/Integral-Donovan-Finiteness-over-Witt-Vectors","pdf":"https://github.com/openai/math/blob/main/preprints/Integral-Donovan-Finiteness-over-Witt-Vectors-September-25-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Integral-Donovan-Finiteness-over-Witt-Vectors-September-25-2026","tags":["modular-representation-theory","block-theory","finite-groups"],"score":0,"title":"Integral Donovan Finiteness over Witt Vectors","domain":"Algebra","family":"203","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.RA","summary":"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 $`W(\\overline{\\mathbb F}_p)`$. 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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Donovan's conjecture over fields and complete mixed-characteristic DVRs"}