3 problems

Properness conjecture for perfect objects.

Let $X$ be a proper scheme of dimension $d$ over a field $k$, and let $L_1,\ldots,L_d$ be line bundles on $X$. Let $\langle L_1,\ldots,L_d\rangle$ denote the thick subcategory of…

Let $Y$ be a proper scheme of dimension $n$. A locally free sheaf $\mathscr{E}$ on $Y$ has rank $n$ and top Chern number $c_n(\mathscr{E})$. Large top Chern number conjecture. Any…