A graded Buchweitz-Greuel-Schreyer rank conjecture is shown equivalent to a new sheaf-cohomology lower bound on non-Fano hypersurfaces, with a new exact Betti-number-to-cohomology formula as the bridge.
Brown and Tobias Dyckerhoff, Topological K -theory of equivariant singularity categories , Homology Homotopy Appl
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Ranks of matrix factorizations and sheaf cohomology
A graded Buchweitz-Greuel-Schreyer rank conjecture is shown equivalent to a new sheaf-cohomology lower bound on non-Fano hypersurfaces, with a new exact Betti-number-to-cohomology formula as the bridge.