4 problems

Acyclicity criterion. When $n\equiv 1\bmod 4$, $X_{2,n,c}$ is acyclic for asymptotically almost every primitive $c\in\mathbb{F}_n^*$. When $n\equiv 3\bmod 4$, $X_{2,n,c}$ is acycli…

Let the parameters and divisor class be as in the preceding proposition, so that $v=ds+d'f-r_1e_1-\cdots-r_me_m$ satisfies $d'\ge d\ge r_1+r_2$, $r_1\ge r_2\ge\cdots\ge r_m\ge0$, a…

Let $\Delta$ be a simplicial complex. Say that $\Delta$ is $k$-uply acyclic if the link of every face of dimension at most $k-2$ is acyclic. The face poset of $\Delta$ is the poset…

Let $f:X\to Y$ be an integral surjection. A scheme is acyclic with respect to a Grothendieck topology if its higher cohomology with coefficients in every abelian sheaf for that top…