Decidability of derived Morita equivalence for semifree DGAs
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Can derived Morita equivalence be decided for semifree noncommutative differential graded algebras over a nontrivial computable unital commutative ring? The target is undecidability in this class.
Why it matters and what counts as progress
Why it matters: It tests the limits of algorithmically classifying derived module categories of noncommutative differential graded algebras.
What counts as progress: An undecidability reduction for derived Morita equivalence in the stated semifree noncommutative DGA class, or a decidable restricted class.
How the problem developed
- 2026 · Open problem [1]
R. İnanç Baykur, Robion C. Kirby and Daniel Ruberman, editors K3 Problem 5.16 asks whether equivalence tests for semifree DGAs are decidable, separating noncommutative from graded-commutative cases.
- 28 Apr 2026 · Reported undecidability theorem [2]
Ciprian Manolescu and Nick Rozenblyum Reported undecidability of derived Morita equivalence for semifree noncommutative DGAs over nontrivial Turing-computable commutative rings.
AI contribution
Undecidability problems for semifree DG algebras
For semifree noncommutative differential graded algebras over a nontrivial computable unital commutative ring, stable tame isomorphism, quasi-isomorphism and derived Morita equivalence are undecidable.
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