For perfect complexes with power torsion homology, the paper proves level_R F ≥ dim R - dim R/I + 1 and shows the bound is optimal for Koszul complexes.
Avramov, Ragnar-Olaf Buchweitz, Srikanth B
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A lower bound on levels with applications to Koszul Complexes
For perfect complexes with power torsion homology, the paper proves level_R F ≥ dim R - dim R/I + 1 and shows the bound is optimal for Koszul complexes.