Undecidability problems for semifree DG algebras

Abstract

We prove that the stable tame isomorphism, quasi-isomorphism, and derived Morita equivalence problems for semifree noncommutative differential graded algebras (DGAs) are all undecidable. This resolves half of Problem 5.16 from the K3 Problem List in Low-Dimensional Topology. We present two solutions, both obtained (essentially autonomously) by Gemini Deep Think / Aletheia.