A dg-algebra admits a balanced dualizing dg-module exactly when its degree-zero cohomology algebra admits a balanced dualizing complex, which holds precisely under condition χ and finite local cohomological dimension.
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Existence of balanced dualizing dg-modules
A dg-algebra admits a balanced dualizing dg-module exactly when its degree-zero cohomology algebra admits a balanced dualizing complex, which holds precisely under condition χ and finite local cohomological dimension.