OpenAI reports Donovan’s conjecture over algebraically closed fields

For every algebraically closed field K of characteristic p>0 and every fixed bound on defect-group order, blocks of finite groups represent only finitely many K-linear Morita-equivalence classes.

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Understanding the problem

Read the background

For every algebraically closed field K of characteristic p>0 and every fixed bound on defect-group order, blocks of finite groups represent only finitely many K-linear Morita-equivalence classes.

Why it matters

If correct, resolves Donovan’s finiteness conjecture over algebraically closed fields without restricting defect groups to be abelian.

What counts as progress

Are there only finitely many block Morita types for bounded defect groups?

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