6 problems

Ideal Generation Conjecture. The conjecture holds if

Characterization conjecture. Every element of the destabilization set of $U$ comes from vanishing conditions on the map $M$. Moreover, knowing the destabilization set of $U$ is equ…

Vanishing-entry conjecture. Every element of the destabilization set of $U$ arises by imposing vanishing conditions on entries of the map $M$ of the minimal free resolution of $U$.

The minimal-resolution conjecture. Under these hypotheses, every sheaf destabilized at the second-last wall in this way has the asserted Gaeta resolution and block-matrix structure…

The surface Minimal Resolution Conjecture. The Betti table has the displayed shape

Lorenzini's Minimal Resolution Conjecture. The Betti table has only two nonzero rows, and in those rows